The displacement-time(x−t) graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t=43s is
A
√332π2 cm/s2
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B
−π232 cm/s2
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C
π232 cm/s2
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D
−√332π2 cm/s2
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Solution
The correct option is D−√332π2 cm/s2 From given graph, amplitude (A)=1 cm
Time period (T)=8 s ∴ω=2π8=π4 rad/s
Dispalcement of the particle, x=Asinωt
Acceleration , a=−ω2A sin ωt
at t=43 s, a=−π216×1×sin (π4×43) =−π216sin(π3) =−√332π2cm/s2