a spring whose constant is 100N/m has a 0.4 kg block attached to it. The spring

Question

a spring whose constant is 100N/m has a 0.4 kg block attached to it. The spring and mass sit on a horizontal frictionless surface. The block is pulled 0.3 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 the expressions for the displacements, velocity, and acceleration as function of time.

Explanation / Answer

3) ? = v(k/m) = v ( 100/0.4) = 15.81 rad/s 1) frequency = ?/2p = 15.81/2p = 2.517 hertz 2) time period = 1/frequency = 1/2.517 = 0.397 s 4) amplitude = x =0.3 m 5) max velcoity = ?.X = 15.81 * 0.3 = 4.743 m/s 6) acceleration = ?^2.X = 15.81^2 * 0.3 = 74.98 m/s^2 7) displacement = 0.3sin (15.81t) velocity = 4.743cos(15.81t) acceleration = -74.98 sin(15.81t)

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