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Questions  

Consider a body executes periodic motion given by  2sin2t+π4m. Then we can  concluded that

a
It represents SHM with time period of  πs, amplitude of 2 m and phase of  π4
b
motion is periodic but not SHM, With time period of  πs, amplitude of 2 m and  phase of  π4
c
Motion represents SHM with time period of 2 s, amplitude 1m and phase of  π4
d
Represents SHM with time period of 2s, amplitude 2m and phase of π4

detailed solution

Correct option is A

The given equation 2sin2t+π4 can be compared with  y=A​  sin(ω  t+ϕ). This  shows that the body executes a simple harmonic motion. Time period can be  determined from  'ω' of the given equation. On comparison of  2sin2t+π4 with   A​  sin(ω  t+ϕ)., We get  ω=2  rad  s−1,A=2mWe know that ω=2πt=2πT&ϕ=π4∴2=2πTT=πsHence, We condude that time period T=πs amplitude A=2m and phase  ϕ=π4

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