Questions
The displacement of a particle is represented by the equation . The motion of the particle is
detailed solution
Correct option is B
Given displacement of simple harmonic oscillator is y=3cosπ/4-2ωtto find Velocity differentiate above equation with respect to time t, then V=dydt=ddt3cosπ/4-2ωt V=6ωsinπ/4-2ωtAcceleration a=dVdt=ddt6ωsinπ/4-2ωt=6ω×-2ωcosπ/4-2ωt=−12ω2cosπ/4-2ωt=−4ω23cosπ/4-2ωta=-4ω2yaα-y.Hence, due to negative sign motion is SHM.Clearly, from the equation ω1=2ω [standard equation y=acos(ωt+ φ )]2πT1=2ωT1=πω. So motion is SHM with period π/ω .Talk to our academic expert!
Similar Questions
A horizontal platform with an object placed on it is executing S.H.M. in the vertical direction. The amplitude of oscillation is . What must be the least period of these oscillations, so that the object is not detached from the platform
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