Question

What is the equation describing the motion of a mass on the end of a spring which is stretched 8. 8 cm from equilibrium and then released from rest, and whose period is 0. 66 s ? assume that the displacement at the start of the motion is positive.

Answer 1

The equation describing the motion of a mass on the end of a spring is y=8.8cos(3πt)

Simple Harmonic motion is same like to and fro motion. Body is moving a certain distance from a point on both sides freely.

We know very well that equation of Simple Harmonic Motion is given by y=Acos(wt)

• where y is the displacement of body,
• A the Amplitude of body
• w is the angular frequency of body
• and t is time .

We also know very well that angular frequency=2π/Total time

=>ω=2π/T

We have T=0.66sec

Therefore,ω=2π/0.66

           =>ω=(2×3.14)/0.66

             =>ω=6.28/0.66

             =>ω=9.515 =3π(approximately)

Now, we have also given that spring is stretched to 8.8cm.

Therefore, amplitude(A)=8.8cm

Therefore, y=8.8cos(3πt)

Hence, the equation is y=8.8cos(3πt)

To know more about Simple Harmonic Motion, visit here:

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