Solving SHM: Max Speed & Accel. for 1.11kg Mass on Spring

In summary, the conversation discusses the calculation of maximum speed and maximum magnitude of acceleration for a mass undergoing simple harmonic motion on a frictionless surface with a horizontal force applied. The equations for calculating these values are ωA for maximum speed and Aω^2 for maximum acceleration, where ω is the angular frequency and A is the amplitude of displacement.
  • #1
Becca93
84
1
Homework Statement
A mass of 1.11 kg on a spring rests on a frictionless surface and has a horizontal force of magnitude 1.23 N applied to it to keep it 1.3 m from the equilibrium. The mass undergoes simple harmonic motion when released.

What is the maximum speed? What is the maximum magnitude of acceleration? What is the magnitude of acceleration of the mass when it's displacement is one fifth of the maximum value?


The attempt at a solution

From previous questions in the series,
k = 0.946
f = 0.147
ω = (2)(pi)(0.147)

My issue is that I don't know how to go about solving for maximum speed or maximum magnitude of acceleration.

Any advice?
 
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  • #2


If you check your SHM equations you should find that max speed is when displacement = 0
and max acceleration is when displacement is a maximum (ie at the amplitude)
Max speed = ωA and max acceleration = Aω^2
Hope this gets you into it
 
  • #3


technician said:
If you check your SHM equations you should find that max speed is when displacement = 0
and max acceleration is when displacement is a maximum (ie at the amplitude)
Max speed = ωA and max acceleration = Aω^2
Hope this gets you into it

I was missing those equations in my notes. I've got the answers now. Thank you very much!
 

FAQ: Solving SHM: Max Speed & Accel. for 1.11kg Mass on Spring

What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium, and the motion follows a sinusoidal pattern.

How do you find the maximum speed in SHM?

The maximum speed in SHM can be found by taking the square root of the ratio of the maximum potential energy to the mass of the object. The formula is vmax = √(2kA^2/m), where k is the spring constant, A is the amplitude, and m is the mass.

What is the maximum acceleration in SHM?

The maximum acceleration in SHM occurs at the equilibrium point and is equal to the maximum force divided by the mass of the object. The formula is amax = Fmax/m = kA/m, where k is the spring constant and A is the amplitude.

How does the mass affect the maximum speed and acceleration in SHM?

The maximum speed and acceleration in SHM are directly proportional to the square root of the mass. This means that as the mass increases, the maximum speed and acceleration also increase. This can be seen in the formula vmax = √(2kA^2/m) and amax = kA/m, where m is the mass.

What factors can affect the maximum speed and acceleration in SHM?

The maximum speed and acceleration in SHM can be affected by the spring constant, amplitude, and mass. Changes in any of these factors can alter the maximum speed and acceleration. Other factors that can affect SHM include external forces, friction, and air resistance.

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