Question

The displacement of an object attached to a spring and excutes simple harmonic motion is given by x = 2×10⁻²cos2πt metre. The time at which the maximum speed first occures is ? ​

Answer 1

Explanation:

Given, displacement x=2×10

−2

cosπt

The magnitude of velocity , v=∣

dt

dx

∣=2π×10

−2

sinπt

So, the velocity will be maximum when sinπt=1 where πt=

2

π

,

2

3π

,..

So for first maximum, πt=

2

π

or t=0.5s

Answer 2

x=Acosωt; dx/dt =−Aωsinωt

∣dx/dt∣ is maximum when ωt= π/2

here ω=π

∴t= π/2π

= 0.5 sec

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