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Vaibhav Mathur Grade: 12
        

A system is composed of 2 blocks of mass m1,m2 connected by a massless spring with  spring constant k.The blocks slide on a frictionless plane.The unstretched length of spring is l.Initially m2 is held so that the spring is compressed to l/2 and m1 is forced against a stop.M2 is released at t=0.Find the motion of the center of mass of the system as a function of time.

6 years ago

Answers : (1)

Chetan Mandayam Nayakar
312 Points
										

till spring assumes its stress free length, m2 executes SHM and m1 is stationary. the angular frequency is ω=√(k/m2),


the equation of motion of m2 in the SHM is x=l-(l/2)cos(ωt)


centre of mass=m2l(1-(cos(ωt)/2))/(m1+m2) for 0≤t≤(π/2)√(m2/k)


after that kinetic energy of centre of mass =kl2/8=(m1+m2)v2/2, v=(l/2)√(k/(m1+m2))


centre of mass =l+(t-(π/2)√(m2/k))(l/2)√(k/(m1+m2)) for t>(π/2)√(m2/k)

6 years ago
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