An object of mans m is undergoing linear SHM according to x=0.2 sin (3.0t) m. Find the velocity and acceleration of the mass when it is +5 cm from its mean position.
A
±0.58 m/s,0.45 m/s2
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B
±0.8 m/s,1.8 m/s2
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C
±0.58 m/s,−0.45 m/s2
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D
±0.8 m/s,0.45 m/s2
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Solution
The correct option is C±0.58 m/s,−0.45 m/s2 Given, x=0.2 sin (3.0t)∴A=0.2 m;ω=3 rad/s At x=5 cm, v=±ω√A2−x2 =±3√(0.2)2−(0.05)2 =±0.58 m/s a=−ω2x=(−3)2(0.05) =−0.45 m/s2