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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 29th December 2021, 11:09 AM
Answered by 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



 



Answered by Expert 29th December 2021, 12:15 PM
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