A mass hanging from a vertical spring is in simple harmonic motion as given by the following position function, where t is measured in seconds and s is in inches: s(t)=−3cos(πt+π4). Determine the position of the spring at t=1.5 s. Find the velocity of the spring at t=1.5 s.

The position and velocity of the spring is −2.12 inches and -6.66 ft/s.

Explanation:

Given that,

The position function,

We need to calculate the position of the spring at t = 1.5 s

Using position function

Put the value of t in the function

We need to calculate the velocity of the spring

Using position function

On differentiating

Put the value into the formula

Hence, The position and velocity of the spring is −2.12 inches and -6.66 ft/s.

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note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.