A metal cylinder with a mass of 1.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The cylinder is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 18.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The cylinder oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 90 N/m (b) What is the frequency of the oscillations (in Hz)? 1.44 ✔ Hz (c) What is the maximum speed of the cylinder (in m/s)? 1.81 ✓ m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? x= ± 0 m (e) What is the maximum acceleration of the cylinder? (Enter the magnitude in m/s².) 16.37 ✓ m/s² (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? x = ± 0.2 m (g) What is the total mechanical energy of the oscillating spring-cylinder system (in J)? (h) What is the speed of the cylinder (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the cylinder (in m/s2) when its position is equal to one-third of the maximum displacement from equilibrium? m/s²
A metal cylinder with a mass of 1.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The cylinder is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 18.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The cylinder oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 90 N/m (b) What is the frequency of the oscillations (in Hz)? 1.44 ✔ Hz (c) What is the maximum speed of the cylinder (in m/s)? 1.81 ✓ m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? x= ± 0 m (e) What is the maximum acceleration of the cylinder? (Enter the magnitude in m/s².) 16.37 ✓ m/s² (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? x = ± 0.2 m (g) What is the total mechanical energy of the oscillating spring-cylinder system (in J)? (h) What is the speed of the cylinder (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the cylinder (in m/s2) when its position is equal to one-third of the maximum displacement from equilibrium? m/s²
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter2: Newtonian Mechanics-single Particle
Section: Chapter Questions
Problem 2.52P: A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where...
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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.
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Please solve parts g to i
Transcribed Image Text:A metal cylinder with a mass of 1.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The cylinder is pulled to a distance of 0.200 m
from its equilibrium position, held in place with a force of 18.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The cylinder oscillates along the
x-axis, where x = 0 is the equilibrium position.)
(a) What is the spring constant (in N/m)?
90
N/m
✔
(b) What is the frequency of the oscillations (in Hz)?
1.44
Hz
(c) What is the maximum speed of the cylinder (in m/s)?
1.81
m/s
(d) At what position(s) (in m) on the x-axis does the maximum speed occur?
x = ± 0
m
(e) What is the maximum acceleration of the cylinder? (Enter the magnitude in m/s².)
16.37
m/s²
✔
(f) At what position(s) (in m) on the x-axis does the maximum acceleration occur?
x = ± 0.2
m
(g) What is the total mechanical energy of the oscillating spring-cylinder system (in J)?
J
(h) What is the speed of the cylinder (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium?
m/s
(i) What is the magnitude of the acceleration of the cylinder (in m/s2) when its position is equal to one-third of the maximum displacement from equilibrium?
m/s²
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