Total energy of a particle executing SHM is 3 J. A maximum force of 1.5 N acts on it. Time period and epoch of the SHM are 2s and `30^(0)` respectively. Establish the equation of this SHM and also find the mass of the particle.

Explanation

Total energy = `1/2momega^(2)A^(2)=3" "...(1)`
Maximum force = mass `xx` maximum acceleration
`=mxxomega^(2)A=1.5" "...(2)`
Dividing (1) by (2) we get, `1/2A=2or,A=4m`
Time period, T = 2 s
`therefore" "omega=(2pi)/T=(2pi)/2=pi"rad"*s^(-1)`
Epoch, `alpha=30^(@)=pi/6`.
So, the equation of SHM is `x=Asin(omegat+alpha)`
or, `x=4sin(pit+pi/6)m`
Again from equation (2),
`m=1.5/(omega^(2)A)=(1.5)/(pi^(2)*4)=0.038kg`.