A mass hanging from a vertical spring is somewhat more complicated than a mass a

Question

A mass hanging from a vertical spring is somewhat more complicated than a mass attached to a horizontal spring because the gravitational force acts along the directn of motion. Therefore, the restoring force of the oscillations is not provided by the spring force alone, but by the net force resulting from both the spring force and the gravitational force. Ultimately, however, the physical quantities of motion (position, velocity, and acceleration) for a vertical mass on a spring exhibit the same oscillations as a horizontal mass on a spring. A 100 g mass hangs from a vertical spring as shown In the picture. The measuring stick shows us the vertical y positlon of the bottom of the spring wlth the origin ( 0) at the top of the spring. Note that the positive y direction is downward. The 100 g mass is at rest at the position shown y 50 an The dashed l ne in the picture y 30 cm indicates the unstretched resting length of the spring. The mass is pulled down 6 cm, stretching the bottom of the spring to y 56 cm, and then released so that it begins oscillating. 1. What are the equilibrium position and amplitude of the oscillations? =30 A=26 cm x cm 2. Is the spring force equal to zero at the equilibrium point? Explain why or why not

Explanation / Answer

The equilibrium position of spring mass system is, y=50 cm.

The amplitude of oscillation ,A=6 cm.

At the equilibrium the spring force is not equal to zero. The spring force is equal to weight of object.

The spring force ,F =mg. Here m-mass, g - acceleration due to gravity.

Spring force and weight that is gravitational force acts equal in magnitude and opposite in direction on object at

Equilibrium so net force on it zero.

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