An object of mass m is attached by two stretched springs (stiffness k s and rela

Question

An object of mass m is attached by two stretched springs (stiffness ks and relaxed length L0) to rigid walls, as shown in the figure below. The springs are initially stretched by an amount (L L0). When the object is displaced to the right and released, it oscillates horizontally. Starting from the Momentum Principle, find a function of the displacement x of the object and the time t that describes the oscillatory motion.

(a) What is the period of the motion? (Use the following as necessary: m and ks. Note that the s is lowercase.)

T =

(b) If L0 were shorter (so that the springs are initially stretched more), would the period be larger, smaller, or the same?

The period would be larger. T depends on the length and stiffness of each spring.

The period would be smaller. T depends on the length and stiffness of each spring.    

The period would be the same. T depends on the mass of the object and the stiffness of each spring.

Explanation / Answer

a.) Let the mass be displaced by a small distance x to tthe right of the equlibrium position, in this situation, the spring on left gets elongated by equal length x and that on the right gets compressed by the same length.the force acting on mass are then,

F1= -kx

F2=-kx

net force = -2kx

T = 2pi *Sqrt(m/2k)

2.)The period would be the same. T depends on the mass of the object and the stiffness of each spring.

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