The equation of a particle executing SHM is x=(5m)sin[(π s−1)t+π3]. What is its amplitude, time period, maximum speed and velocity. At t = 1s?
A typical equation representing SHM looks like x=A sin(ω t+ψ0)
Where x represents displacement
ω represents angular frequency
ψ0 represents initial phase
A represents amplitude
In the question we have x=(5m)sin[(π s−1)t+π3]
So let's compare both! In a simple glance one can see
A=5m, ω=π s−1 and ψ0=π3
Time period 2πω=2ππ=2s
Now what about velocities?
Let's differentiate the equation dxdt=(5m)π cos{(π s−1)t+π3}
v=(5π)mcos{(π s−1)t+π3}
We know that dxdt means velocity. To find the maximum velocity we can argue that cos has maximum value of 1 so Vmax=5π ms−1. To
find velocity at t = 1s, let's substitute for t in velocity equation we get V1s=−5π ms−12.