The displacement of a particle executing SHM is given by- x-0-01sin 100-t-0-05- The time period is-

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Relating Circular Motion to SHM

The displacem...

Question

The displacement of a particle executing $S H M$ is given by: $x = 0.01 sin 100 π (t + 0.05)$ . The time period is:

0.01 s e c

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0.02 s e c

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0.1 s e c

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0.2 s e c

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Solution

The correct option is B $0.02 s e c$
Given: $x = 0.01 sin 100 π (t + 0.05) = 0.01 sin (100 π t + 5)$
S.H.M equation is $x = A sin (ω t + ϕ)$
Comparing the above equations, we get
$A = 0.01$ , $ω t = 100 π t$
$\Rightarrow ω = 100 π$
$\Rightarrow \frac{2 π}{T} = 100 π$
$\Rightarrow \frac{1}{T} = 50$
$\Rightarrow T = \frac{1}{50} \times \frac{2}{2} = \frac{2}{100} = 0.02$ secs

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The displacement of a particle executing SHM is given by: x=0.01sin100π(t+0.05). The time period is:

The correct option is B 0.02 secGiven:x=0.01sin100π(t+0.05)=0.01sin(100πt+5)S.H.M equation is x=Asin(ωt+ϕ)Comparing the above equations, we getA=0.01, ωt=100πt⇒ω=100π⇒2πT=100π⇒1T=50⇒T=150×22=2100=0.02 secs

The displacement of a particle executing $S H M$ is given by: $x = 0.01 sin 100 π (t + 0.05)$ . The time period is: