Question

for a particle in simple harmonic motion amplitude of displacement is a and amplitude of velocity is v find the amplitude of acceleration?​

Answer 1

α

v

2

Since the amplitude of displaement of the SHM is α, the SHM would have the form,

x=αsin(ωt+ϕ)

Thus v=

dt

dx

=ωαcos(ωt+ϕ)

⟹ amplitude of velocity=ωα=v

⟹ω=

α

v

Similarly, acceleration of the particle in SHM is

dt

dv

=−ω

2

αsin(ωt+ϕ)

⟹ amplitude of acceleartion=ω

2

α=(

α

v

)

2

α=

α

v

2

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