if friction is set to zero and on planet Earth. Now, if you attach a mass to the spring from its initial equilibrium position, it vibrates forever in simple harmonic motion. Why doesn't it come to rest after stretching by a distance 'd'; proportional to the weight of the mass, when the spring's restoring force cancels out the weight of the mass? How will you measure the equilibrium position? How can you attach the mass to the spring so that it doesn't oscillate when you let go?

Well, it falls to d, but it has velocity, which takes it further than d, finally, the velocity is zero, but now the spring pulls it up, and is goes and goes.

Compare it to a pendulum, you raise it, and behold, it passes the equilibrium position at the bottom, and moves upward on the other side.

thank u so much it makes sense

In a situation where there is zero friction and the only force acting on the mass-spring system is due to gravity, the spring will indeed oscillate forever in simple harmonic motion. Let's break down the reasons for the perpetual motion.

When the mass is attached to the spring and stretched by a distance 'd', the gravitational force acting on the mass is balanced by the restoring force of the spring. At this point, the system is in equilibrium, meaning the net force on the mass is zero. However, due to the absence of friction or any other dissipative force, there is nothing to dampen the oscillations. As a result, the system will continue to oscillate back and forth indefinitely.

To measure the equilibrium position of the mass-spring system, you can use a ruler or measuring tape. Start by placing the mass-spring system on a stationary surface, ensuring it is not disturbed by any external forces. Then, measure the distance from the rest position (when the spring is unstretched) to determine the equilibrium position.

To prevent the mass from oscillating when you let go, you can fix it in place by attaching it securely to the rest position of the spring. One way to achieve this is by using a clamp or a hook to hold the mass in place at the desired location on the spring. This way, when you release the mass, it will not move further and disrupt the equilibrium.