Question

The displacement of a particle from its mean position ( in meter) is given by $Y=0.2\sin \left(10\pi t+1.5\right)\cos \left(10\pi x+1.5\right).$. The motion of the particle is

• A. Periodic but not SHM
• B. Non-periodic
• C. SHM with period 0.1 sec
• D. SHM with period 0.2 sec

Answer 1

The correct option is C SHM with period 0.1 sec

Given

$Y=0.2sin(10\pi t+1.5)cos(10\pi x+1.5)$ --------------(i)

We know , $sin2\theta =2sin\theta cos\theta$

Thus multiplying and dividing eq (i) with 10

We get , $Y=0.1sin2(10\pi t+1.5)$

Or, $Y=0.1sin(20\pi t+3)$----------(ii)

The equation of a particle having SHM is given by $Y=Asin(\omega t+\varphi )$

Comparing with eq (ii) we see that the particle exhibits SHM .

$\omega t=20\pi$

Or $\frac{2\pi }{T}t=20\pi$

Or,$T=0.1t$

Thus ,the particle shows SHM with a time period of 0.1 sec .(Answer)