Question

How to prove that x= 5sin(wt+theta) is the equation of shm

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+ 6π )

a) A =Amplitude = 5 m

b) ϕ = Initial phase constant =

6

π

c) Angular frequency, ω=π rad/sec

∴ Time period, T= ω2 = ππ2 =2 sec

d) Maximum Speed, v

max

=∣Aω∣=∣5×2∣=10 m/sec

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Answer 2

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+ 6π )

a) A =Amplitude = 5 m

b) ϕ = Initial phase constant =

6

π

c) Angular frequency, ω=π rad/sec

∴ Time period, T= ω2 = ππ2 =2 sec

d) Maximum Speed, v

max

=∣Aω∣=∣5×2∣=10 m/sec