A compact, dense object with a mass of 4.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The object is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 29.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The object oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? N/m (b) What is the frequency of the oscillations (in Hz)? Hz (c) What is the maximum speed of the object (in m/s)? m/s

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Chapter1: Units, Trigonometry. And Vectors
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A compact, dense object with a mass of 4.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The object is pulled to a distance
of 0.200 m from its equilibrium position, held in place with a force of 29.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The object
oscillates along the x-axis, where x =
O is the equilibrium position.)
(a) What is the spring constant (in N/m)?
N/m
(b) What is the frequency of the oscillations (in Hz)?
Hz
(c) What is the maximum speed of the object (in m/s)?
m/s
(d) At what position(s) (in m) on the x-axis does the maximum speed occur?
X = +
(e) What is the maximum acceleration of the object? (Enter the magnitude in m/s2.)
m/s?
(f) At what position(s) (in m) on the x-axis does the maximum acceleration occur?
X = ±
m
(g) What is the total mechanical energy of the oscillating spring-object system (in J)?
(h) What is the speed of the object (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 object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium?
m/s?
Transcribed Image Text:A compact, dense object with a mass of 4.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The object is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 29.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The object oscillates along the x-axis, where x = O is the equilibrium position.) (a) What is the spring constant (in N/m)? N/m (b) What is the frequency of the oscillations (in Hz)? Hz (c) What is the maximum speed of the object (in m/s)? m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? X = + (e) What is the maximum acceleration of the object? (Enter the magnitude in m/s2.) m/s? (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? X = ± m (g) What is the total mechanical energy of the oscillating spring-object system (in J)? (h) What is the speed of the object (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 object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s?
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