Question

weighted block attached to a string is dropped and bobs up and down due to the spring. The blocks height follows a simple harmonic motion given by the equation s=cost, where the height is in cm, and t is time in seconds. Find the first three derivatives. What do these derivatives represent in terms of the scenario ?​

Answer 1

First Derivative: s'(t) = -sin(t), Second Derivative: s''(t) = -cos(t), Third Derivative: s'''(t) = sin(t)

How to find the first three derivatives

The first three derivatives of the equation s = cos(t), along with their interpretations in terms of the scenario:

First Derivative:

s'(t) = -sin(t)

This represents the velocity of the block.

Second Derivative:

s''(t) = -cos(t)

This represents the acceleration of the block.

Third Derivative:

s'''(t) = sin(t)

This represents the rate of change of acceleration