Question

The equation of particle executing simple harmonic motion is x = (5m) sin [(pis^(-1))t+(pi)/(3)]. Write down the amplitude, time period and maximum speed. Also find the velocity at t = 1 s.

Answer 1

The general equation of SHM is

x=ASin(ωt+ϕ)

where A is the amplitude

ω is the angular frequency

ϕ is the initial phase constant

Here

x=(5m)Sin(πs

−1

t+

6

π

)

a) A =Amplitude = 5 m

b) ϕ = Initial phase constant =

6

π

c) Angular frequency, ω=π rad/sec

∴ Time period, T=

ω

2π

=

π

2π

=2 sec

d) Maximum Speed, v

max

=∣Aω∣=∣5×2∣=10 m/sec

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