I'm doing calc1 by myself right now and not sure where to start with this problem: Here are the questions: An object attached to a spring swings vertically around its equilibrium position. The height of the object relative to its position of equilibrium is given by the following function: h(t)=(e^-(x/10)*100sin(x)-10cos(x))/101 *(See photo i have provided)* a) Give the object movement for the first 10 seconds. I know i can find the speed of an object if i have it's acceleration. But how do i find it's movement fom it's height? I have done the integral of the height's equation and it's -(100e^-(x/10)(20sin(x)+99cos(x))/10201+Constant b) Give the total distance traveled by the object during the first 10 seconds I would assume this is something along the lines of finding the final positition of the object and the initial position and substracting them? c) Give the total distance that will be traveled by the object from time t = 0. at this point i am clueless to what i should find I think i'm getting things mixed up and would apreciate help. Thanks.

I'm doing calc1 by myself right now and not sure where to start with this problem: Here are the questions: An object attached to a spring swings vertically around its equilibrium position. The height of the object relative to its position of equilibrium is given by the following function: h(t)=(e^-(x/10)100sin(x)-10cos(x))/101 (See photo i have provided)* a) Give the object movement for the first 10 seconds. I know i can find the speed of an object if i have it's acceleration. But how do i find it's movement fom it's height? I have done the integral of the height's equation and it's -(100e^-(x/10)(20sin(x)+99cos(x))/10201+Constant b) Give the total distance traveled by the object during the first 10 seconds I would assume this is something along the lines of finding the final positition of the object and the initial position and substracting them? c) Give the total distance that will be traveled by the object from time t = 0. at this point i am clueless to what i should find I think i'm getting things mixed up and would apreciate help. Thanks.

Related questions

Q: A mass is oscillating horizontally on a spring. At the locations A, B, C, D, and E, photogates are…

A: Given: The potential energy at A AP.E.=40 J

Q: Forces F→1, F→2, and F→3 act on the structure of the figure, shown in an overhead view. We wish to…

A: Given : a = 1.90 m b = 3.27 m c = 1.31 m F1⇀= 38.1 N F2⇀ = 18.9 N F3⇀ = 2.05 N

Q: Problem 10: The restoring force in a Hooke's Law spring is a conservative force, and hence, the work…

A: (C) Total energy of mass E= 8 joule Equilibrium position of mass is at x=18 CM At x=14cm & 22 cm…

Q: The disk is rotating horizontally, and the block has a weight of 2 lb. Friction between the block…

A: The block is at rest means that there is no net force acting on the block. Hence, the centrifugal…

Q: If one oscillation has 6.5 times the energy of a second one of equal frequency and mass, what is the…

Q: The figure depicts the displacement of an oscillator x[m], as a function of time t[s] 0 -1 -2 -3 0…

A: We will answer the questions by analysing the given figure. The detailed steps are given below.

Q: A 10-kg steel ball is tied to a string attached to a ceiling. If the length of the string is 45 cm,…

A: Given, A 10-kg steel ball is tied to a string attached to a ceiling. Length of string , l = 45 cm =…

Q: Given that the Spring energy is ½ kx2, where x is the displacement of the spring from its…

A: Given data: Spring energy (U) = (1/2)kx2 x is displacement, k is spring constant The unit of spring…

Q: Calculate the kinetic energy of the mass 3 s into the motion, in J.

A: Mass, m=0.13Kg Stiffness of spring, k=366N/m The displacement from the equilibrium, x=0.26m

Q: The motion of a particle is given by x(t) = (24cm)cos(10t) where t is in s. what is the first time…

A: Givenx(t)=(24 cm)cos(10 t)velocity, v(t)=dxdt =-(240 cm)sin(10 t)maximum…

Q: You just installed a new swing in your backyard. When you are swinging, you are 168 cm from the…

Q: The motion of a particle connected to a spring is described by x = 10 sin (πt). At what time (in s)…

Q: Write down an expression for the net force on a simple pendulum of the mass malong (tangentially to)…

Q: A spring is stretched 34.5 cm beyond its equilibrium length. How much energy has been transferred to…

A: Given data: Stretch in spring (x) = 34.5 cm = 0.345 m Spring constant (k) = 86.8 N/cm = 8680 N/m…

Q: The motion of a particle is given by x(t) = (25cm)cos(10t) where t is in s. what is the first time…

A: Given, The motion of the particle is given by, x(t) = 25 cm cos10 t -----(1) we have to evaluate…

Q: 6. A linear spring of force constant k is used in a phys- ics lab experiment. A block of mass m is…

A: Solution:-Given thatLinear spring constant =kmass of the block =mresulting frequency=f

Q: The cylinder has a mass of 70 kg and is released from rest when h = 0. Each spring has a stiffness k…

Q: Problem 2: A fisherman has caught a fish on his pole, and to keep the pole steady he has to apply…

A: Consider the Figure shown below.

Q: Problems 5 & 6 refer to the mass-spring oscillator depicted in the figure on the right. The block…

A: Mass of the block, m = 0.35 kg Spring constant, k = 45 N/m Initial position at time t = 0 is -20 cm…

Q: derive ω = αt + ω0

A: Sorry for the inconvenience. As you have posted multiple questions in one question, so as per…

Q: I.A bullet of mass m has a velocity of v, just before it strikes the target of mass M. If the bullet…

A: A compression spring is also known as an open-coil helical spring that is responsible for offering…

Q: As shown in Figure 1, a block with mass m = 3.5 kg is placed on a horizontal surface at position A,…

Q: 1. A frictionless spring-mass system slides back and forth with simple harmonic motion on a…

A: Answers: a) zero b) When the speed is minimum the spring is either extended by 4.5 cm or compressed…

Q: A slingshot, consisting of a leather pouch attached to two rubber bands which are tied to the prongs…

A: Consider the slingshot as a spring as a spring. Hence according to the conservation of energy, the…

Q: For the shown system: θ = 54 ∘, k = 640 N/m , m = 3 kg , and the unstretched spring length is 290 mm…

Q: In reality, the product r*v remains fixed when the string is pulled in. That means that v increases…

A: Assume that that the product of the radius r and velocity v remains constant when the string is…

Q: A point mass m is hanging from a massless spring attached at one end at a point O. The mass can…

Q: A pendulum of length / and mass m is mounted on a block of mass M. The block can move freely without…

A: The degree of freedom is the minimum number of independent coordinates or variables that are used to…

Q: As shown in the diagram above, a simple pendulum of length 2.5 meters is composed with a string with…

Q: A pendulum bob swings through an arc 40 cm long on its first swing. Each swing thereafter, it swings…

A: For the first swing the distance =40cmthe second swing the distance =0.8×40cmthe third swing the…

Q: In the final section of the lab, the student is asked to investigate the energy distribution of the…

A: Given, mass , m = 295.0 g = 0.295 kg spring constant , k = 13.44 N/m equilibrium position = 21.5 cm…

Q: A .20 kg ball is attached to a vertical spring. The spring constant is 28N/m. the ball supported…

Q: Consider a situation in which a pendulum made from a wooden sphere. The mass of the pendulum is 100…

A: Given : Mass of the pendulum, m =100 g=100×10-3 kg Length of the pendulum, l=1m Question :…

Question

I'm doing calc1 by myself right now and not sure where to start with this problem:

Here are the questions:

An object attached to a spring swings vertically around its equilibrium position. The height of the object relative to its position of equilibrium is given by the following function: h(t)=(e^-(x/10)*100sin(x)-10cos(x))/101 *(See photo i have provided)*

a) Give the object movement for the first 10 seconds.

I know i can find the speed of an object if i have it's acceleration. But how do i find it's movement fom it's height? I have done the integral of the height's equation and it's -(100e^-(x/10)(20sin(x)+99cos(x))/10201+Constant

b) Give the total distance traveled by the object during the first 10 seconds

I would assume this is something along the lines of finding the final positition of the object and the initial position and substracting them?

c) Give the total distance that will be traveled by the object from time t = 0.

at this point i am clueless to what i should find

I think i'm getting things mixed up and would apreciate help. Thanks.

1
(3.241, 0.7124)
10
· 100 sin (x) – 10 cos (x)
-100e
'(20 sin (x) + 99 cos (x))/(10201)
-0.5
(9.524, 0.3801)
3
4
3
4
6.
9
10
11
--0.5
(6.383, –0.5204)
powered by
desmos
(0.1, –0.9754)
+
國

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A spring of unstretched length L and spring constant k is attached to a wall and an object of mass M resting on a frictionless surface (see figure). The object is pulled such that k M the spring is stretched a distance A then released. Let the +x- direction be to the right. L. What is the position function x (t) for the object? Take x = 0 to be the position of the object when the spring is relaxed, and make the phase angle as simple as possible. の= 4 T, where T is 3 What is the velocity v, of the object at t = Ux = the period? Write the expression using fractions, not decimal values. What is the acceleration a, of the object at t = T? ax =
A wheel is free to rotate about its fixed axle. A spring is attached to one of its spokes at distance r from the axle. Assuming that the wheel is a hoop of mass m and radius R, what is the angular frequency w of small oscillations of this system in terms of m, R, r, and the srping constant k? What is w if r =R and if r = 0? Thank you for the help. I think I'm tripping myself up with using r in the equations.
A convenient way of measuring g without having to drop things is to use a pendulum. I took a pendulum of length 112 cm, and found that it oscillated 12 times in 25.34 sec (I really did this!). What value does this suggest for g?
A 2.6kg mass is a attached to a spring with a stiffness of 410N/m. In the picture on the left side, the system is in equilibrium. A student then displaces the spring downward to the position as shown. Neglect friction and drag. What is the period of the harmonic motion? unit What is the frequency of the harmonic motion? unit How many cycles would the system make in 55s? (You may answer with a decimal) 37cm What is the minimum length (L) of the spring as it oscillates? cm How far does the mass travel during one period? cm 44cm 00000
If you did the previous question right, you hopefully got an expression for yo. You may notice that you can simplify the differential equation a little bit: d'y k (y – yo) dt2 т The parameter yo now plays the roll of the "relaxed length". A better term may be "equilibrium value for y". But mathematically, it's identical to a relaxed length with the spring as the only force. We continue using this equation: y(t) = Y0 + A cos(wt + y) Now, solve for A (in cm) with these parameters. Again, if you need more information, enter -100000. The parameters are: •m = 200 grams • Yo = (equilibrium value) = 40 cm • k = (spring constant) = 0.03 N/cm
In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with particles or rigid bodies that can be treated as particles, the Lagrangian can be defined as: L = T-V where T is the kinetic energy of the particle, and V the potential energy of the particle. It is also advised to start with Cartesian coordinates when expressing the kinetic energy and potential energy components of the Lagrangian e.g. T = m (x² + y² + 2²). To express the kinetic energy and potential energy in some other coordinate system requires a set of transformation equations. 3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum of length 1, mass m, free to with angular displacement - i.e. angle between the string and the perpendicular is given by: 3.2 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 L = T-V = ²² +mg | Cos Write down the Lagrange equation for a single generalised coordinate q. State name the number of generalised coordinates in problem 3.1. Hence write…
An m-mass pendulum is connected to a spring with the spring constant k through the massless rope along I as in the picture. x, i wiwww. k point y =0 m The spring is then given a deviation of x, so it moves at a speed of x. Assume point y = 0 is parallel to the spring, so that the potential energy of the pendulum negative value. If the pendulum has a deviation of 0, specify: Lagrangian equation of the system
Imagine you've constructed a pendulum at home and measured the length of the rope and the period. The goal here is to create a graph where the slope corresponds to the gravitational acceleration constant. For that you have to get an X and a Y. First, you have these 2 equations as a starting point: T= 2π/ω and ω= sqrt(g/L). Play with the equations to construct an equation for a linear graph with the form: Y=mX+b where the slope m=g. Identify clearly what X and Y represent. The equation should look like: ? = g(? + ?)
Write down the expression for period of a pendulum of length I and the gravitational field strength g. Please use Il * II for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate. For square root and power please use sqrt(A*B) and (A*B)^2. Please use the "Display response" button to check you entered the answer you expect. T=
Initially, a pendulum swings through an arc of 10 feet. On each successive swing, the length of the arc is 0.8 of the previous length. (a) What is the length of the arc of the eighth swing? (b) On which swing is the length of the arc first less than 5 feet? (c) After 15 swings, what total length will the pendulum have swung? (d) When it stops, what total length will the pendulum have swung?
Two identical springs are connected in series as shown, each spring has a spring constant of 30 N/m. What is the spring constant of the overall two-spring system, in N/m? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.
in simple pendulum experiment , my doctor gave me this table . he want me to fill the empty values and find the slope ( ΔT2/ΔL ) to calcuate the gravity constant by this formula : g= 4π2/slope . but i could't do it please help