1) Maximum
2) Maximum
Explanation:
The force acting on a mass on a spring is given by Hooke's law; in magnitude:
[tex]F=kx[/tex]
where
F is the force
k is the spring constant
x is the displacement
Also we know from Newton's second law that we can write
[tex]F=ma[/tex]
where
m is the mass
a is the acceleration
So we can write the equation as
[tex]ma=kx[/tex] (1)
From this relationship, we see that the acceleration is directly proportional to the displacement.
On the other hand, we know that the total mechanical energy of the system mass-spring is constant, and it is given by
[tex]E=\frac{1}{2}kx^2+\frac{1}{2}mv^2=const.[/tex] (2)
where the first term is the elastic potential energy while the second term is the kinetic energy, and where
v is the velocity of the mass
From eq. (2), it is clear that when displacement increases, velocity decreases, and vice-versa; however, from eq.(1) we also know that acceleration is proportional to the displacement.
Therefore this means that:
- When acceleration increases, velocity decreases
- When acceleration decreases, velocity increases
Therefore, the two answers here are:
- When the acceleration of a mass on a spring is zero, the velocity is at a maximum
When the velocity of a mass on a spring is zero, the acceleration is at a maximum
