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

Question

The displacement of a particle from its mean position (in m ) is given by, y=0.2sin (10 π t + 1.5 π ) cos ⁡ (.10π t+1.5π ). The motion of particle is (A) periodic but not S.H.M (B) non-periodic (C) simple harmonic motion with a period 0.1 s (D) simple harmonic motion with a period 0.2s

Tardigrade Admin · Accepted Answer

y=0.2sin (10 π t + 1.5 π )cos â¡ (.10π t+1.5 π .) =0.1sin 2 (.10π t+1.5π .) [∵ sin 2 A = 2 sin A cos A] =0.1sin (20 π t + 3.0 π ) ∴ Time period T=(2 π /ω )=(2 π /20 π )=(1/10)=0.1 s

Q. The displacement of a particle from its mean position (in $m$ ) is given by, $y = 0.2 s in (10 π t + 1.5 π) cos (10 π t + 1.5 π) .$ The motion of particle is

periodic but not S.H.M

non-periodic

simple harmonic motion with a period $0.1 s$

simple harmonic motion with a period $0.2 s$

$y = 0.2 s in (10 π t + 1.5 π) cos (10 π t + 1.5 π)$
$= 0.1 s in 2 (10 π t + 1.5 π)$
$[∵ s in 2 A = 2 s in A cos A]$
$= 0.1 s in (20 π t + 3.0 π)$
$∴$ Time period $T = \frac{2 π}{ω} = \frac{2 π}{20 π} = \frac{1}{10} = 0.1 s$

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

periodic but not S.H.M

non-periodic

simple harmonic motion with a period 0.1s

simple harmonic motion with a period 0.2s

y=0.2sin(10πt+1.5π)cos⁡(10πt+1.5π) =0.1sin2(10πt+1.5π) [∵sin2A=2sinAcosA] =0.1sin(20πt+3.0π) ∴ Time period T=ω2π​=20π2π​=101​=0.1s

Q. The displacement of a particle from its mean position (in $m$ ) is given by, $y = 0.2 s in (10 π t + 1.5 π) cos (10 π t + 1.5 π) .$ The motion of particle is

simple harmonic motion with a period $0.1 s$

simple harmonic motion with a period $0.2 s$

$y = 0.2 s in (10 π t + 1.5 π) cos (10 π t + 1.5 π)$
$= 0.1 s in 2 (10 π t + 1.5 π)$
$[∵ s in 2 A = 2 s in A cos A]$
$= 0.1 s in (20 π t + 3.0 π)$
$∴$ Time period $T = \frac{2 π}{ω} = \frac{2 π}{20 π} = \frac{1}{10} = 0.1 s$