First slide

Oscillation motion

Question

The amplitude and time period of a particle of mass 0.1 kg executing simple harmonic motion are 1m and 6.28s, respectively. Find its (i) angular frequency, (ii) acceleration and (iii) velocity at a displacement of 0.5m.

Moderate

A

1 rad/sec, –1 ms^–2, $\large \sqrt 3 m{s^{ - 1}}$
B

$\large 0.5\,rad/\sec ,\,\, - 0.5m{s^{ - 2}},\,\frac{{\sqrt 3 }}{2}m{s^{ - 1}}$
C

$\large 1\,rad/\sec ,\,\, - 0.5m{s^{ - 2}},\frac{{\sqrt 3 }}{2}m{s^{ - 1}}$
D

$\large 1\,rad/\sec ,\,\, - 0.5m{s^{ - 2}},\sqrt 3 m{s^{ - 1}}$

Solution

$\large m\, = \,\,0.1kg;\,A\, = 1m;\,T\, = \,6.2\sec ;\,y\, = \,0.5m$
$\large \omega \, = \,\frac{{2\pi }}{T}\, = \,\frac{{2 \times 3.14}}{{6.28}}\, = \,1rad/\sec$
Acceleration a = – w²y
$\large a\, = \, - {\left[ {\frac{{2\pi }}{T}} \right]^2};\,a\, = \,{\left[ {\frac{{2 \times 3.14}}{{6.28}}} \right]^2} \times 0.5\, = \,{1^2} \times 0.5$
$\large = \, - {1^2} \times 0.5\, = \, - 0.5m/{s^2}$
$\large \Rightarrow \,velocity\, = \,\omega \sqrt {{A^2} - {y^2}} \, = \,(1)\sqrt {{1^2} - {{(0.5)}^2}}$
= $\large \sqrt {1 - {{\left( {\frac{1}{2}} \right)}^2}} \, = \,\sqrt {1 - \frac{1}{4}} \, = \,\frac{{\sqrt 3 }}{2}m/\sec$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App