A spring with k = 35.5 N/m has a mass of 5.50 kg attached to it. An external force F = (4.40 N)sin[(6.80 s−1)t] drives the spring mass system so that it oscillates without any resistive forces. What is the amplitude of the oscillatory motion of the spring-mass system?

A = 0.02 m

Explanation:

The spring constant, k = 35.5 N/m

The attached mass, m = 5.50 kg

The expression for the external force, F =  (4.40 N)sin[(6.80 s⁻¹)t].....(1)

The general expression for the external force, F = F₀ sin (wt).............(2)

Comparing equations (1) and (2):

The forced frequency,

F₀ = 4.40 N

The natural frequency can be calculated using the formula:

The amplitude of oscillation of a spring-mass system in the steady state:

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