Question

29. The instantaneous displacement of a simple pendulum oscillator is given by acos(wt+π/4)
its speed will be maximum at time?​

Answer 1

at t = π/(4ω) , speed of particle will be maximum.

The instantaneous displacement of a simple pendulum oscillator is given as y = acos(ωt + π/4)

differentiating with respect to time,

dy/dt = -ωasin(ωt + π/4)

here, dy/dt is the velocity of particle executing SHM.

so, speed of particle = | dy/dt | = ωasin(ωt + π/4)

so, dy/dt will be maximum when sin(ωt + π/4) will be maximum i.e., 1

so, sin(ωt + π/4) = 1 = sin(π/2)

⇒ωt + π/4 = π/2

⇒ωt = π/4

⇒t = π/(4ω)

hence, at t = π/(4ω) , speed of particle will be maximum.

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Answer 2

$\huge\bold\purple{Answer:-}$

The instantaneous displacement of a simple pendulum oscillator is given as y = acos(ωt + π/4)

differentiating with respect to time,

dy/dt = -ωasin(ωt + π/4)

here, dy/dt is the velocity of particle executing SHM.

so, speed of particle = | dy/dt | = ωasin(ωt + π/4)

so, dy/dt will be maximum when sin(ωt + π/4) will be maximum i.e., 1

so, sin(ωt + π/4) = 1 = sin(π/2)

⇒ωt + π/4 = π/2

⇒ωt = π/4

⇒t = π/(4ω)