The maximum speed and acceleration of a particle executing simple harmonic motion are 10cms−1 and 50cms−2. Find the position(s) of the particle when the speed is 8cm−1.
Max speed
v=Aω=10 ...(1)
max acceleration
a=Aω2=50 ...(ii)
Dividing (ii) with (i)
ω=5 ...(iii)
substituting (iii) in (i)
10=A×5
A=2 ...(iv)
We derived the relation between v and x as.
v=ω√A2−x2
To find x when v = 8
8=5√4−x2
x2=4−6425x=√3625=±65=±1.2cm