Explanation:
It is given that,
Spring constant of the spring, k = 15 N/m
Amplitude of the oscillation, A = 7.5 cm = 0.075 m
Number of oscillations, N = 31
Time, t = 15 s
(a) Let m is the mass of the ball. The frequency of oscillation of the spring is given by :

Total number of oscillation per unit time is called frequency of oscillation. Here, 


m = 0.0895 kg
or
m = 89 g
(b) The maximum speed of the ball that is given by :





Hence, this is the required solution.
The answer is C) the density of the rock
Density of rock is the dependent variable, because it depends on the temperature. The temperature can’t be the dependent variable because ,the density of a rock does not have magical powers that can change temperature of a room. However changing the temperature of the room ,will change the density of the rock. Hope this helps !
Answer:
Advantage:
Apparent solar time gives the exact location of sun in the sky according to your precise location.
Disadvantage:
As the apparent solar time changes with the change in longitude. It is very difficult to track these changes in longitude. Hence, it is almost impossible to make plan for events.
Improvement in situation:
Situation can be improved using mean solar time because due to this people living in the longitude band agree upon a standard time. In this way, it is easy to plan for events.
Find the amount of work that the spring does. This can be found using the equation 1/2kx^2. Then, you must set that equal to the amount of kinetic energy the car has. This is possible thanks to the work-energy theorem.
1/2kx^2 = 1/2mv^2
Solve to find velocity. Remember, the spring is displaced .15 m, not 15!
To find the acceleration, use F = ma. The force being applied to the car is kx, and you know the mass. You do the math.
For problem C I don't know, haven't done that yet in my class. Sorry!