Question

A particle executing SHM completes 1200 oscillations per minute and passes the mean position with a velocity of 3.14 m/s.to find the maximum displacement of a particle from the mean position .also obtain the displacement equation of the particle if its displacement is zero at instant t=0.

Answer 1

Step 1, Given data

Frequency = 1200 oscillations per minute

Or, $f=1200\times \frac{1}{60}=20Hz$

Maximum velocity = 3.14 $or\pi$ m/s

Step 2,

Now we can write

$A\times 2\pi f-\pi$

Or, $A-\frac{1}{2f}-\frac{1}{20}=0.05$

Hence the maximum displacement is 0.05 m

Maximum displacement is the amplitude of the SHM

Now,

The equation of the particle can be written as

$x-0.05sin\left(40\pi t\right)$