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a particle execute a shm of period 10sec& amplitude of 1.5 m calculate it's max acceleration & velocit
Asked by thaduripranitha | 29 Dec, 2021, 11:09: AM
Expert Answer
Equation for displacement x of particle undergoing SHM is given as
x = A cos ( ω t + Φ ) .............................. (1)
where A is amplitude , ω = ( 2π / T ) is angular frquency , T is period of oscillation and Φ is initial phase .
Velocity v of particle is obtained by differentiating eqn.(1)
v = dx/dt = - A ω sin( ω t + Φ ) .............................. (2)
Acceleration a of particle is obtained by differentiating eqn.(2)
a = dv/dt = - A ω2 cos( ω t + Φ ) .............................. (3)
We get magnitude of maximum velocity from eqn.(2) as
vm = A ω = 1.5 × ( 2π / 10 ) = 0.3π m/s
We get magnitude of maximum acceleration from eqn.(3) as
vm = A ω2 = 1.5 × ( 2π / 10 )2 = 0.06 π2 m/s2
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