A particle mass 10 gm is executing shm with an amplitude of 0.5 m and periodic time of pi/s secThe max value of the force acting on the particle

Dear pallavi

x=Xsinwt         where w=2 pi/T          and T=pi/5

 =.5sin 10t

w=√k/m

so k=w²m

       =10² *10

        =1000   gm/sec²

maximum force=kx

                       =1000*.5  m*gm/sec²

                        =.5 kg m/sec²

Dear Pallavi,

We know for shm motion of the particle  its displacement is given by y= y₀ sin ωt  Where  ω = 2π/T =  2π/π = 2 and amplitude

y₀ = 0.5 m

thus aceeleration on the particle is given by a=  d²y/d²t =   - y₀ * ω² * sin ωt

Maximum acceleration is a_max = - y₀ * ω²  = - 2 m/s²

Thus maximum force in magnitude = | m* a_max| = 0.02 N

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