Question

A mass hanging from a spring undergoes vertical simple harmonic motion.1) Where in the motion is the velocity equal to zero?At the point where the spring is unstretched.At the highest point in the oscillation.At the lowest point in the oscillation.

Answer 1

In vertical SHM, such as a mass on a spring, the velocity is zero at the highest and lowest points of oscillation. At equilibrium, where the spring is not stretched or compressed, the mass has maximum speed.

Step-by-step explanation:

In simple harmonic motion (SHM) such as a mass attached to a vertical spring, the velocity of the mass is equal to zero at the highest and lowest points of its oscillation. This occurs because kinetic energy is fully converted into potential energy at these points. In the case of a mass hanging from a spring undergoing vertical simple harmonic motion, the velocity is equal to zero at two points in the motion:

• At the highest point in the oscillation, when the mass momentarily comes to a stop before reversing direction.

• At the lowest point in the oscillation, when the mass momentarily comes to a stop before moving upward again.

The equilibrium position, marked as x = 0, is where the spring is neither stretched nor compressed. At this position, the mass has maximum speed because all potential energy is converted into kinetic energy. The physics of SHM highlight that the spring exerts forces that depend on its displacement and motion characteristics such as amplitude and period are determined by the mass and stiffness of the spring.

Answer 2

At the highest point and at the lowest point the velocity of the mass hung on a spring = 0

Step-by-step explanation:

Simple Harmonic Motion ( S.H.M) : Simple harmonic motion can be defined as a type of motion were a body vibrates or moves to and fro along a straight line under the influence of a force, so that the acceleration of the body towards a fixed point (equilibrium position) is proportional to its distance or displacement from that point. Examples of bodies undergoing simple harmonic motion are

⇒ The motion of a mass hung on a spring.

⇒ The motion of a simple pendulum

⇒ The motion of a loaded test - tube in a liquid.

Motion of a mass hung on a spring:When a mass is hung to one end spring and other end is firmly clamped to a rigid support.(i)When the mass is in motion, (ii)it pulled down to its lowest point, passes through it equilibrium position (iii) goes to its highest point.

(1) At the lowest and the highest point during the motion of a mass hung a spring, the velocity = 0

(2) At the equilibrium point or unstretched position the velocity is maximum