Question

What is the effective mass of the spring?

Answer 1

Hint : A spring is a pliable item that may be used to store mechanical energy. Spring steel is the most common material used to make springs. There are several spring patterns to choose from. Coil springs are commonly referred to as "coil springs" in everyday usage. When a typical spring is compressed or extended from its resting position, it exerts an opposing force that is roughly proportionate to the length change (this approximation breaks down for larger deflections). A spring's rate, or spring constant, is equal to the change in force it exerts divided by the change in deflection.

Complete Step By Step Answer:
The spring in a genuine spring–mass system has a non-zero mass m. The kinetic energy of the spring is not equal to $\dfrac{1}{2}m{{v}^{2}}$ because not all of its length moves at the same velocity v as the suspended mass M. As a result, the frequency of oscillation cannot be determined by merely adding m to M, and the effective mass of the spring is defined as the mass that must be added to M in order to accurately anticipate the system's behaviour.
When employing an ideal spring with uniform linear density, the effective mass of the spring in a spring-mass system is $\dfrac{1}{3}$ of the mass of the spring and is independent of the direction of the spring-mass system (i.e., horizontal, vertical, and oblique systems all have the same effective mass). This is because the period of motion around the equilibrium point is unaffected by external acceleration. The kinetic energy of the spring may be used to calculate its effective mass. When employing an ideal spring with uniform linear density, the effective mass of the spring in a spring-mass system is a $\dfrac{1}{3}$ of the mass of the spring and is independent of the direction of the spring-mass system.

Note :
The spring-mass system may be used for a wide range of tasks. It may be used to replicate human tendon movements for computer images, as well as deformation of the foot skin. Springs are manufactured from a variety of elastic materials, with spring steel being the most prevalent. Small springs can be wrapped from pre-hardened material, whereas bigger springs are fabricated from annealed steel and then hardened. Phosphor bronze and titanium are utilised for parts that require corrosion resistance, while beryllium copper is used for springs that conduct electrical current (because of its low electrical resistance).