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?
The reason the mass attached to the spring does not come to rest after stretching by a distance 'd' is because of the concept of simple harmonic motion. In simple harmonic motion, the restoring force provided by the spring is directly proportional to the displacement from equilibrium position, but it is also in the opposite direction. Therefore, as the mass moves away from the equilibrium position, the spring exerts a force that pulls it back towards the equilibrium position, causing it to oscillate back and forth.
When the spring's restoring force cancels out the weight of the mass, it means that the net force acting on the mass is zero. However, this does not mean the mass will come to rest because the mass already has some initial velocity due to the displacement from equilibrium. This initial velocity allows the mass to continue moving, leading to the oscillation.
To measure the equilibrium position of the spring, you can use a ruler or a measuring tape. The equilibrium position is the position of the mass when no external force is acting on it and it is at rest. It is the position where the force due to the spring is equal to the weight of the mass but in the opposite direction. You can measure the distance from the reference point (e.g., the bottom of the spring) to the equilibrium position to determine the displacement 'd'.
To attach the mass to the spring so that it doesn't oscillate when you let go, you need to ensure that the mass is at the equilibrium position initially. This can be done by carefully adjusting the position of the mass until it is perfectly balanced and not stretched or compressed. Once the mass is at the equilibrium position, you can attach it to the spring using a clip or hook, making sure there is no initial displacement or force acting on the mass when you let go. This will prevent it from oscillating when released.