A puck of mass m is mounted between identical springs with force constant k and

Question

A puck of mass m is mounted between identical springs with force constant k and can slide back and forth on the level frictionless surface as shown. The springs have negligible mass. The puck is displaced from its equilibrium position at Y to position X, at which point it is released from rest. It then oscillates back and forth between positions X and Z. Determine whether each of the following statements is true or false. Show a calculation or explain briefly the reason for each answer. The restoring force exerted by the springs is always proportional to the displacement and in the opposite direction. True or False? Explain. This system is an example of a simple harmonic oscillator. True or False? Explain. If the mass m were doubled while leaving the spring constants k and the initial displacement fixed the period of oscillation would double. True or False? Explain. If the mass m were doubled while leaving the spring constants k and the initial displacement fixed the maximum kinetic energy of the puck would double. True or False? Explain. If the initial displacement were doubled while leaving the spring constants k and the mass m fixed the maximum kinetic energy would double. True or False? Explain. If the left spring constant k were doubled while leaving all other parameters fixed the time required for the puck to travel from Y to X would be shorter than the time required for the puck to travel from Y to Z. True or False? Explain.

Explanation / Answer

A) true, because F= -kx,the more is the extension, the more will be force.

B)true, here the springs are in parallel, their combination has spring constant of 2k

C)False, T = 2 pi* sqrt(m/k) period is proportional to square root of mass.

D)False, Maximum KE =0.5*(2k)x^2...i.e. independent of mass.

E)False, maximum KE will become 4 times as energy is proportional to x^2

F) False, it will be equal as effective K =2k+k = 3k....for combination.

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