The angle (with respect to the vertical) of a simple pendulum is given by 0 Omcos[(5.88 rad/s)t + $]. If at t = 0,0 = 0.0450 rad and de/dt = -0.160 rad/s, what are (a) the phase constant o and (b) the maximum angle 0m? (Hint: Don't confuse the rate de/dt at whic changes with the w of the SHM.) %3D

The angle (with respect to the vertical) of a simple pendulum is given by 0 Omcos[(5.88 rad/s)t + $]. If at t = 0,0 = 0.0450 rad and de/dt = -0.160 rad/s, what are (a) the phase constant o and (b) the maximum angle 0m? (Hint: Don't confuse the rate de/dt at whic changes with the w of the SHM.) %3D

Name: The angle (with respect to the vertical) of a simple pendulum is give
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: The angle (with respect to the vertical) of a simple pendulum is given by 0= 0mcos[(5.88 rad/s)t + ø]. If at t = 0, 0 = 0.0450 rad and d0/dt = -0.160 rad/s, what are (a) thephase constant o and (b) the maximum angle 0m? (Hint: Don't confuse the rate

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 29P: The angular position of a pendulum is represented by the equation = 0.032 0 cos t, where is in...

See similar textbooks

Related questions

Q: The height attained by a weight attached to a spring is s(t)=-4 cos 10t inches after t seconds.…

A: Height attained by a weight attached to a spring is s(t) = -4cos(10t)

Q: he harmonic motion function d(t) = 5cos(2 t), in which d is measured in centimeters and t is…

Q: he work done by the spring from t = 0 to t = π/4ω starting from eqn. 1.

A: The position of a simple harmonic oscillator with mass m is given by x(t) = A sin ωt. where A is the…

Q: Two mass-spring systems are oscillating with the same total energy, but system A's am- plitude is…

A: Given. Two spring mass system are oscillating with same total energy. The amplitude of system a is…

Q: Period of a pendulum A standard pendulum of length L that swings under the influence of gravity…

A: Given: A standard pendulum of length L swinging under only the influence of gravity (no resistance)…

Q: Because of dissipative forces, the amplitude of an oscillator decreases 3.96% in 10 cycles. By what…

Q: Use the approximation T 2 x s √ = (₁ + 4/²) to to approximate the period (in seconds) of a pendulum…

Q: Q. 20 : If the length of the simple pendulum is increased by 44 %, then what is the change in time…

A: To find- Change in periodic time=? Given- Original length (L1)=L New length (L2)=44%L1+L1…

Q: oscillator needs to accomplish 20 The angular of this oscillator is A horizontal 20 seconds…

A: The time required to complete one oscillation is called the time period. Here 20 oscillations occurs…

Q: A man wants to measure the how high is the ceiling of a room by hanging a long pendulum from the…

A: Given: no. of oscillations in 1min = 14 times

Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

Topic Video

Question

The angle (with respect to the vertical) of a simple pendulum is given by 0
= 0mcos[(5.88 rad/s)t + ø]. If at t = 0, 0 = 0.0450 rad and d0/dt = -0.160 rad/s, what are (a) the
phase constant o and (b) the maximum angle 0m? (Hint: Don't confuse the rate d0/dt at which 0
changes with the w of the SHM.)
%3D
Pivot
point
L.
Is= Le
F.cose
Fg sine
(a)
(6)

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
A grandfather clock has a pendulum length of 0.7 m and mass bob of 0.4 kg. A mass of 2 kg falls 0.8 m in seven days to keep the amplitude (from equilibrium) of the pendulum oscillation steady at 0.03 rad. What is the Q of the system?
If the speed of the observer is increased by 5.0%, what is the period of the pendulum when measured by this observer?
For each expression, identify the angular frequency , period T, initial phase and amplitude ymax of the oscillation. All values are in SI units. a. y(t) = 0.75 cos (14.5t) b. vy (t) = 0.75 sin (14.5t + /2) c. ay (t) = 14.5 cos (0.75t + /2) 16.3
The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, 6"max, to the maximum angular velocity, e'max, is rt s^(-1). What is the time needed for the pendulum to complete two oscillations?
In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, 6'max, to the maximum angular velocity, O'max, is Tt s^(-1). What is the time needed for the pendulum to complete one-half oscillation?
O 0.15 sec In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max, to the maximum angular velocity, O'max, is Tt s^(-1). What is the time needed for the pendulum to complete two oscillations? O 1 sec O 2 sec O 4 sec O 0.5 sec O 0.25 sec
In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max, to the maximum angular velocity, O'max, is Tt s^(-1). What is the time needed for the pendulum to complete two oscillations? 4 sec 1 sec 0.5 sec 2 sec 0.25 sec
The period (T) and length (L) values of a simple pendulum found in the table below were obtained experimentally. L(m) T(s) 1 2,01 1,1 2,11 1,2 2,20 1,3 2,29 1,4 2,38 1,5 2,46 1,6 2,54 Knowing that: T=2π√(L/g) and from linearization Y=T, A = 2π/√g , X=L e B=0. Calculate: a) The value of the angular coefficient of the line that best fits the experimental points of a T chart (y-axis) x √L (x-axis). (don't forget the error propagated) b) Value g with the correct amount of significant digits.
In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max, to the maximum angular velocity, e'max, is tt s^(-1). What is the time needed for the pendulum to complete two oscillations? 4 sec 2 sec 1 sec 0.5 sec 0.25sec