Simple Harmonic Motion Maxiumum Velocity

• richardstan
In summary, the conversation is about calculating the maximum speed and acceleration of a mass oscillating on a light vertical spring. The time period and amplitude of oscillation are given, and the person mentions having an equation for speed and a value for frequency. They also ask if the maximum speed occurs when the value of cos(2(Pi)ft) = 1, to which the other person confirms and adds a smiley face.

richardstan

Hi, wondering if someone could help me with the following question.

A mass is hung from the lower end of a light vertical spring, whose upper end is fixed. The mass is pulled down and released and the time period of the oscillating system is measured. If the time period is 0.25s and the amplitude of oscillation is 30mm, calculate:

i.)the maximum speed
ii.)the maxiumum acceleration

I have an equation for the speed:

ds/dt = A 2(pi)f cos(2(Pi)ft)

i have a value for the frequency, is the maximum speed when the value of cos(2(Pi)ft) = 1?
Thanks
Richard.

You got it.

Hello Richard,

Thank you for your question. In simple harmonic motion, the maximum velocity occurs when the displacement is at its maximum value, which is the amplitude A. This means that the maximum speed of the mass is equal to the amplitude multiplied by the frequency: vmax = A * f.

In this case, the amplitude is given as 30mm and the frequency can be calculated using the formula f = 1/T, where T is the time period of 0.25s. Therefore, the maximum speed would be vmax = (30mm) * (1/0.25s) = 120mm/s.

To calculate the maximum acceleration, we can use the formula a = -(2*pi*f)^2 * x, where x is the displacement. In this case, the maximum acceleration would be amax = -(2*pi*(1/0.25s))^2 * (30mm) = -7539.82 mm/s^2.

I hope this helps answer your question. Let me know if you have any further questions. Good luck with your calculations!

Best,

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium position, with a restoring force that is directly proportional to the displacement from the equilibrium position.

What is maximum velocity in simple harmonic motion?

Maximum velocity in simple harmonic motion is the highest speed reached by the object during its oscillations. It occurs at the equilibrium position, where the restoring force is zero and the object has the maximum kinetic energy.

How is maximum velocity related to amplitude in simple harmonic motion?

The maximum velocity in simple harmonic motion is directly proportional to the amplitude of the oscillations. This means that as the amplitude increases, so does the maximum velocity. This relationship is described by the equation vmax = ωA, where vmax is the maximum velocity, ω is the angular frequency, and A is the amplitude.

What factors affect the maximum velocity in simple harmonic motion?

The maximum velocity in simple harmonic motion is affected by the amplitude, angular frequency, and mass of the object. A higher amplitude or angular frequency will result in a higher maximum velocity, while a higher mass will result in a lower maximum velocity.

How is maximum velocity calculated in simple harmonic motion?

The maximum velocity in simple harmonic motion can be calculated using the equation vmax = ωA, where vmax is the maximum velocity, ω is the angular frequency, and A is the amplitude. Alternatively, it can be calculated using the equation vmax = 2πfA, where f is the frequency and A is the amplitude.