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A trolley of mass m is connected to two identical springs, each of force constant k, as shown in fig. The trolly is displaced from its equilibrium position by a distance x and released. The trolly executes simple harmonic motion of period T. After some time it comes to rest due to friction. The total energy dissipated as heat is (assume the damping force to be weak)

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a

12kx2

b

kx2

c

4π2mx2T2

d

mx2T2

answer is B.

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Detailed Solution

Two springs are connected in parallel equivalent spring constant is – 2K.Total energy 122Kx2=kx2The final energy of the system = 0 Hence the total energy dissipated is = kx2

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A trolley of mass m is connected to two identical springs, each of force constant k, as shown in fig. The trolly is displaced from its equilibrium position by a distance x and released. The trolly executes simple harmonic motion of period T. After some time it comes to rest due to friction. The total energy dissipated as heat is (assume the damping force to be weak)