Answer:

Explanation:
The equation for centripetal acceleration is
.
We know the wheel turns at 45 rpm, which means 0.75 revolutions per second (dividing by 60), so our frequency is f=0.75Hz, which is the inverse of the period T.
Our velocity is the relation between the distance traveled and the time taken, so is the relation between the circumference
and the period T, then we have:

Putting all together:

Answer:

Explanation:
The angular frequency of the system is:

The frequency is:


The angular frequency is:


The spring constant is:


Answer:
parabolic path
Explanation:
As the cart reaches the end of the table with a horizontally directed velocity (only horizontal component), the cart will follow a parabolic path given by the combined action of:
(1) kinematic equation for motion under constant velocity in the horizontal direction (linear expression in terms of time), and
(2) kinematic equation for motion under constant acceleration (that of gravity) in the vertical direction (quadratic expression in terms of time)
They transfer energy. Not sure what your choices are but this is a common question