The correct option is C S.H.M with period 0.1 s
Given ,
Displacement of the particle y=0.2sin(10πt+1.5π)cos(10πt+0.5π)
From the above equation, we get
y=0.1[2sin(10πt+1.5π)cos(10πt+0.5π)]
Using, 2 sin A cos B = sin (A + B) + sin (A - B)
we get ,
y=0.1[sin(20πt+2.0π)+sin(π)]
⇒y=0.1sin(20πt+2.0π)
⇒y=0.1sin(20πt)
∴ The particle starts from mean position and executes SHM.
Comparing this with y=Asin(ωt), we get ω=20π ; A=0.1 m
Time period of oscillation, T=2πω=2π20π⇒T=110=0.1 s
Thus, option (c) is the correct answer.