A force F cos (! t) is applied to a spring of negligible mass which is fixed on one end and on the other end has an attached mass m = 1 kg. The spring constant is k = 100 N/m. If the applied force remains constant in magnitude, the amplitude of oscillation of the mass on the spring is maximum when the fre- quency of the applied force (cycles per second) is about

The amplitude is maximum when the frequency is 1.59Hz

Explanation:

This problem is based on the simple harmonic motion of a spring

The period of the motion T is given as

T =2π√m/k

Given data

Attached mass m= 1kg

Spring constant k =N/m

Substituting our data into the equation we have

T =2*3.142√1/100

T=6.284√0.01

T=6.284*0.1

T=0.63sec

But frequency f=1/T

f=1/0.63

f=1.59Hz

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