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```        The equation of motion of a particle started at t = 0 is given by x = 5 sin (20 t + π/3), where x is in centimeter and t in second. When does the particle
a) first come to rest
b) first have zero acceleration
c) first have maximum speed?
```
3 years ago

Kevin Nash
332 Points
```										Sol. . x = 5 sin (20t + π/3)
a) Max. displacement from the mean position = Amplitude of the particle.
At the extreme position, the velocity becomes ‘0’.
∴ x = 5 = Amplitude.
∴ 5 = 5 sin (20t + π/3)
sin (20t + π/3) = 1 = sin (π/2)
⇒ 20t + π/3 = π/2
⇒ t = π/120 sec., So at π/120 sec it first comes to rest.
b) a = ω2x = ω2 [5 sin (20t + π/3)]
For a = 0, 5 sin (20t + π/3) = 0 ⇒ sin (20t + π/3) = sin (π)
⇒ 20 t = π – π/3 = 2π/3
⇒ t = π/30 sec.
c) v = A ω cos (ωt + π /3) = 20 × 5 cos (20t + π/3)
when, v is maximum i.e. cos (20t + π/3) = –1 = cos π
⇒ 20t = π – π/3 = 2 π/3
⇒ t = π/30 sec.

```
3 years ago
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