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The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10–2 cos pt metre.The time at which the maximum speed first occurs is ?

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10–2 cos pt metre.The time at which the maximum speed first occurs is ?

Grade:12

2 Answers

Arun
25763 Points
one year ago
Given, displacement x=2×102cosπt
The magnitude of velocity , v=dtdx=2π×102sinπt
So, the velocity will be maximum when sinπt=1  where πt=2π,23π,..
So for first maximum, πt=2π or t=
Vikas TU
14149 Points
one year ago
x=Acosωt; 
dt/dx
 =−Aωsinωt
  
dt/dx is maximum when ωt= π/2
 
here   ω=π
∴t= π/2π
 = 0.5 sec............................................

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