The displacement of a particle from its mean position (in metre) is given by y = 0.2 sin(10πt+ 1.5π)cos(10 πt+1.5 π). The motion of particle is

y = 0.2 sin(10πt+1.5π)cos(10πt+1.5π)   = 0.1 sin 2(10πt + 1.5 π)    = 0.1 sin(20πt+ 3.0π)[∵ sin 2A = 2 sin A cos A]∴  Time period, T = 2πω = 2π20π = 110 = 0.1 sec