A spring whose spring constant is 120 N/m has a 0.1 kg block attached to it. The

Question

A spring whose spring constant is 120 N/m has a 0.1 kg block attached to it. The spring and mass sit on a horizontal frictionless surface. The block is pulled 0.2 m and released. 1. Find the frequency of the oscillations 2. Find the period of the oscillations 3. Find the angular frequency of the oscillations (w) 4. Find the amplitude of the oscillations. 5. Find the maximum velocity of the block. 6. Find the maximum acceleration of the block. 7. Write ecpressions for the displacement, velocity and acceleraton as functions of time.

Explanation / Answer

Given , k = 120 N/m , m = 0.1 kg , x = 0.2 m

Part A) frequency (f) = (1/2)*(k/m)

f = (1/2)*(120/0.1)

f = 5.51 Hz

Part B) time period (T) = 2(m/k) = 2(0.1/120)

T = 0.181 s

Part C) angular frequency (w) = (k/m)

w = (120/0.1) = 34.64 rad/s

Part D) using conservation of energy

(1/2)*k*x^2 = (1/2)*k*A^2

x = A

So, Amplitude (A) = 0.2 m

Part E) maximum velocity (v) = A*w = 0.2*34.64 = 6.928 m/s

Part F) maximum acceleration (a) = -A*w^2

a = -0.2*34.64^2 = 240 m/s^2

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