A mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s. Find the following part a and b. A) Find the equation of motion, x(t). B) What type of damped motion is this system?
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- 8. A weight of 0.5kg stretches a spring by 0.49m. The spring-mass system is submerged in delicious melted butter with a damping coefficient of y=4. The spring is then lowered by an additional 1.0m and released with velocity 0. There is no external force. Find the function which gives the location of the weight at time t. Note: I have designed this to work out nicely. If it's not working out nicely then you probably got some butter in your calculations.A block of mass m = 2 kg is attached a spring of force constant k = 500 N/m as shown in the figure below.The block is initially at the equilibrium point at x = 0 m where the spring is at its natural length. Then theblock is set into a simple harmonic oscillation with an initial velocity 2.5 m/s at x = 0 cm towards right. Thehorizontal surface is frictionless. a) What is the period of block’s oscillation? b) Find the amplitude A of the oscillation, which is the farthest length spring is stretched to. c) Please represent block’s motion with the displacement vs. time function x(t) and draw the motion graphx(t) for at least one periodic cycle. Note, please mark the amplitude and period in the motion graph.Assume the clock starts from when the block is just released. d) Please find out the block’s acceleration when it is at position x = 5cm. e) On the motion graph you draw for part c), please mark with diamonds ♦ where the kinetic energy of theblock is totally transferred to the spring…4.26. Maximum speed * A critically damped oscillator with natural frequency w starts out at position xo > 0. What is the maximum initial speed (directed toward the origin) it can have and not cross the origin?
- A mass M is free to slide along a frictionless rail. A pendulum of length L and mass m hangs from M. 1. Find the equations of motion. 2. Find the total energyFind the equation of simple harmonic motion for a spring mass system where the mass is hanging off the ceiling with the help of a spring if the initial displacement is 1 ft above equilibrium with initial upward velocity of 2 ft/s. Assume w=1. Write in form y=Asin(x+b). Solve for A, x, and b.Below is the depicted graph of the velocity of a block that is connected to a spring with an unspecified mass and a force constant of 80 N/m, undergoing oscillation. The time axis is wrongly marked for 1.6 sec. It should be 1.8 sec. Determine the period, frequency, and angular frequency of oscillation? Calculate the maximum displacement of the mass from equilibrium in centimeters? Just so you know: It does not correspond to the amplitude of the velocity graph. What is the peak acceleration of the mass and identify the moments when it transpires?
- A 330-kg wooden raft floats on a lake. When a 70-kg man stands on the raft, it sinks 3.9 cm deeper into the water. When he steps ff, the raft oscillates for a while. Part A What is the frequency of oscillation? Express your answer using two significant figures. Η ΑΣφ Hz Submit Request Answer Part B What is the total energy of oscillation (ignoring damping)?part A and B3 b) A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 14 ft/s. Find the time (in s) at which the mass attains its extreme displacement from the equilibrium position (the extreme distance after passing the equilibrium position.) Round your answer to two digits after the decimal sign.
- A 2.00 kg, frictionless block s attached to an ideal spring with force constant 350 N/m. At t = 0 the spring is neither stretched nor compressed and the block is moving in the negative direction at 11.0 m/s. Show Transcribed Text Part A G Find the amplitude. Express your answer to three significant figures and include the appropriate units. Show Transcribed Text Part B Go Find the phase angle. Express your answer in radians. Show Transcribed TextDo not copyItem 1 Learning Goal: To understand the application of the general harmonic equation to the kinematics of a spring oscillator. One end of a spring with spring constant k is attached to the wall. The other end is attached to a block of mass m. The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be x = 0. The length of the relaxed spring is L. (Figure 1) The block is slowly pulled from its equilibrium position to some position init> 0 along the x axis. At time t = 0, the block is released with zero initial velocity. The goal is to determine the position of the block (t) as a function of time in terms of w and init It is known that a general solution for the displacement from equilibrium of a harmonic oscillator is x(t) = C cos (wt) + S sin (wt), where C, S, and w are constants. (Figure 2) Your task, therefore, is to determine the values of C and S in terms of w and init Figure 1 of 3 L Xinit win x = 0 Part A Using the…