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Question
A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2. The period of oscillation is ______.
Options
πs.
`π/2` s.
2π s.
`π/t` s.
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Solution
A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2. The period of oscillation is πs.
Explanation:
Let the equation of an SHM is represented by y = a sin ωt
v = `(dy)/(dt)` = a ωcos ωt
⇒ (v)max = aω = 30 ......(i)
Acceleration (A) = `(dx^2)/(dt^2)` = – aω2 sinωt
Amax = ω2a = 60 ......(ii)
In equations (i) and (ii), we get ω(ωa) = 60
⇒ ω(30) = 60
⇒ ω = 2 rad/s
⇒ `(2pi)/T` = 2 rad/s
⇒ T = π sec
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