A mass is attached to the end of a spring and set into oscillation on a horizont

Question

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position of x = +0.150 m. The mass the of block is m = 707 kg, the force constant of the spring is k = 79.3 Nm. Determine the following (a) force component that the spring exerts on the block just before the block is released (Indicate the direction with the sign of your answer.) (b) angular frequency of the resulting oscillatory motion (c) maximum speed of the oscillating mass (d) magnitude of the maximum acceleration of the oscillating mass

Explanation / Answer

given

Amplitude, A = 1.5 m

m = 0.707 kg

k = 79.3 N/m

a) F = -k*A

= -79.3*1.5

= -119 N

b) w = sqrt(k/m)

= sqrt(79.3/0.707)

= 10.6 rad/s

c) Vmax = A*w

= 1.5*10.6

= 15.9 m/s

d) a_max = A*w^2

= 1.5*10.6^2

= 168 m/s^2

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