We have considered two oscillating systems containing a spring: A small cart tha

Question

We have considered two oscillating systems containing a spring: A small cart that oscillates back and forth attached to a spring, and a long stretched spring that carries transverse waves, as shown in the figures on the right. In some sense these two springs are similar but serve different purposes in these two examples. Discuss a way in which they are similar, a way in which they are different, and how we model them differently and why.

We have considered two oscillating systems containing a spring: A small cart that oscillates back and forth attached to a spring, and a long stretched spring that carries transverse waves, as shown in the figures on the right. In some sense these two springs are similar but serve different purposes in these two examples. Discuss a way in which they are similar, a way in which they are different, and how we model them differently and why.

Explanation / Answer

They are similar as in each case they are executing simple harmonic motion. Elastic potential energy will be stored in both cases, some kinetic energy will be there in both cases.

They are different as in 1st case at extreme positions there will only potential energy which is maximum and kinetic energy is zero. At equilibrium position kinetic energy is maximum and potential energy is zero. Time period will be 2(m/k).

In 2nd case potential energy and kinetic energy will be maximum at the same instant and minimum at same instant Particles will execute SHM in vertical direction and wave will propagate along the length of spring.

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