A light spring with a spring constant k = 326 N/mis attached to a vertical wall

Question

A light spring with a spring constant k = 326 N/mis attached to a vertical wall at one end and a block with a mass m = 0.528 kg at the other end. The block rests on a horizontal frictionless surface and is initially at the equilibrium length of the spring. The block is then displaced from the equilibrium position of the spring in such a manner as to stretch the spring by an amount A = 0.170 m and then released. As the block oscillates about the equilibrium position, determine the amount of work done on the block by the spring for the following segments of travel.

(a) the block traveling from the equilibrium position (x = 0) to the position x = A

(at least two decimal places.)

W0 A = ? J

(b) the block traveling from the position x = A to the equilibrium position (x = 0)

(at least two decimal places.)

WA 0 = ? J

(c) the round trip from the equilibrium position (x = 0)to the position x = A and then back to the equilibrium position

W0 A 0 = ? J

Explanation / Answer

spring constant, K=326 N/m

mass, m=0.528 kg

amplitude, A=0.17 m

a)

w=-1/2*k*A^2

=-1/2*326*0.17^2

=-4.71 J

b)

w=1/2*k*A^2

=1/2*326*0.17^2

=4.71 J

c)

work done is zero, W=0

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