Question

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. If the maximum speed of the object is 2.23 m/s, and the maximum acceleration is 5.77 m/s2, find how much time elapses between a moment of maximum speed and the next moment of maximum acceleration.

(Answer should be in seconds)

Hint: What fraction of a period is the time between the maximum speed and acceleration? How are the maximum speed and acceleration related to the period of oscillation?

Answer 1

The time that elapses between a moment of maximum speed and the next moment of maximum acceleration is called half-period.

The relationship between the period of oscillation, T, and the angular frequency, ω, is given by the equation:

T = 2π / ω

The angular frequency, in turn, is related to the acceleration, a, by the equation:

ω = √(a/x)

where x is the amplitude of oscillation.

Since we know the maximum acceleration, we can find the angular frequency:

ω = √(5.77 m/s^2 / x)

And since we know the angular frequency, we can find the period:

T = 2π / ω

We know that half of the period is the time that elapses between a moment of maximum speed and the next moment of maximum acceleration, so we can find the time between these two moments by dividing the period by 2:

t = T/2

Therefore, the time elapses between a moment of maximum speed and the next moment of maximum acceleration is half a period of oscillation.