1. A mass is placed on a frictionless, horizontal table. A spring (k=105 N/m) which can be stretched or compressed, is placed on the table. A 5.8 kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x-2.2 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion in terms of the amplitude 'A', the angular velocity 'aw', and the time 't'. Use the initial conditions to find the value of $ in the equations. Hint: Use the equation editor (orange button in the answer box) and find w in the greek letters. DO NOT USE numerical values for A and w for part (a). For example, a equation could be x(t) = Asin(wt). x() = %3! v(t) = m/ s a(t) = O m/s² (b) Calculate w for this spring-mass system. rad/s W = (c) Find the position, velocity, and acceleration of the mass at time t=3.9 s. Use w up to 4 significant figures in the calculation. Position: x = Velocity: v = Acceleration: a =

1. A mass is placed on a frictionless, horizontal table. A spring (k=105 N/m) which can be stretched or compressed, is placed on the table. A 5.8 kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x-2.2 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion in terms of the amplitude 'A', the angular velocity 'aw', and the time 't'. Use the initial conditions to find the value of $ in the equations. Hint: Use the equation editor (orange button in the answer box) and find w in the greek letters. DO NOT USE numerical values for A and w for part (a). For example, a equation could be x(t) = Asin(wt). x() = %3! v(t) = m/ s a(t) = O m/s² (b) Calculate w for this spring-mass system. rad/s W = (c) Find the position, velocity, and acceleration of the mass at time t=3.9 s. Use w up to 4 significant figures in the calculation. Position: x = Velocity: v = Acceleration: a =

Name: 1. A mass is placed on a frictionless, horizontal table. A spring (k=
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Description: 1. A mass is placed on a frictionless, horizontal table. A spring (k=105 N/m) which can be stretched orcompressed, is placed on the table. A 5.8 kg mass is attached to one end of the spring, the other endis anchored to the wall. The equilibrium posi

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter13: Vibrations And Waves

Section: Chapter Questions

Problem 32P: A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is...

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A small object is attached to the end of a string to form a simple pendulum. The period of its harmonic motion is measured for small angular displacements and three lengths. For lengths of 1.000 m, 0.750 m, and 0.500 m, total time intervals for 50 oscillations of 99.8 s, 86.6 s, and 71.1 s are measured with a stopwatch, (a) Determine the period of motion for each length, (b) Determine the mean value of g obtained from these three independent measurements and compare it with the accepted value, (c) Plot T2 versus L and obtain a value tor g from the slope of your best-fit straight-line graph. (d) Compare the value found in pan (c) with that obtained in pan (b).
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A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (a) What is the force constant of the spring? (b) What are the angular frequency , the frequency, and the period of the motion? (c) What is the total energy of the system? (d) What is the amplitude of the motion? (c) What are the maximum velocity and the maximum acceleration of the particle? (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. (g) Determine the velocity and acceleration of the particle when t = 0.500 s.
Review. A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a frictionless, horizontal surface with an amplitude of 2.00 m. A 6.00-kg object is dropped vertically on top of the 4.00-kg object as it passes through its equilibrium point. The two objects stick together. (a) What is the new amplitude of the vibrating system after the collision? (b) By what factor has the period of the system changed? (c) By how much does the energy of the system change as a result of the collision? (d) Account for the change in energy.
A small object is attached to the end of a string to form a simple pendulum. The period of its harmonic motion is measured for small angular displacements and three lengths. For lengths of 1.000 m, 0.750 m, and 0.500 m, total time intervals for 50 oscillations of 99.8 s, 86.6 s, and 71.1s are measured with a stopwatch. (a) Determine the period of motion for each length. (b) Determine the mean value of g obtained from these three independent measurements and compare it with the accepted value. (c) Plot T2 versus L and obtain a value for g from the slope of your best-fit straight-line graph. (d) Compare the value found in part (c) with that obtained in part (b).
A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension (Fig. P12.65). Find the frequency of vibration of the system for small values of the amplitude (small ). Assume the vertical suspension rod of length L is rigid, but ignore its mass. Figure P12.65