Simple harmonic motion and frequency

In summary, the conversation discusses various statements regarding the effects of changing mass, spring constant, and amplitude on the frequency of a simple harmonic oscillator. It is determined that doubling the mass will halve the frequency, doubling the spring constant will double the frequency, and doubling the amplitude will not change the period but will halve the frequency. However, tripling the amplitude will actually sextuple the frequency. The equations used to calculate these values are also mentioned.
  • #1
ttk3
28
0

Homework Statement


Consider a simple harmonic oscillator made of a mass sliding on a frictionless surface, and attached to a massless linear spring. Which of the following statements are true/false?
True False Quadrupling the mass will halve the frequency.
True False Doubling the spring constant will double the frequency.
True False Tripling the amplitude will sextuple the frequency.
True False Doubling the amplitude will not change the period.
True False Doubling the amplitude will halve the frequency.



Homework Equations



f = (1/ [2pi/sqrt(k/m)])

Vmax = A(2pi/T)

Vmax = A(2pif)

The Attempt at a Solution



using simple numbers I got the answers in this order

True
False
False
False
True

My numbers work out, but I'm wrong...
Any suggestions?
Thanks
 
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  • #2
ttk3 said:
f = (1/ [2pi/sqrt(k/m)])
Does frequency depend on amplitude?
 
  • #3
Ok... So doubling the amplitude doesn't effect the frequency, but I still can't get this question right...

I'm so confused
 
  • #4
Three of those questions refer to amplitude. Check each one.
 

FAQ: Simple harmonic motion and frequency

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point. It follows a sinusoidal pattern and is characterized by a restoring force that is directly proportional to the displacement of the object from its equilibrium position.

What is the frequency of simple harmonic motion?

The frequency of simple harmonic motion is the number of complete oscillations or cycles that occur in one second. It is measured in Hertz (Hz) and is equal to the reciprocal of the period of the motion.

How is the frequency of simple harmonic motion affected by the mass of the object?

The frequency of simple harmonic motion is not affected by the mass of the object. It is solely determined by the restoring force and the stiffness of the system. This means that two objects with different masses but the same restoring force and stiffness will have the same frequency of oscillation.

How does changing the amplitude of simple harmonic motion affect the frequency?

Changing the amplitude of simple harmonic motion does not affect the frequency. The frequency is only dependent on the restoring force and stiffness of the system, and not on the amplitude of the oscillations. This means that the motion will have the same frequency regardless of how large or small the amplitude is.

What are some real-life examples of simple harmonic motion?

Some real-life examples of simple harmonic motion include a swinging pendulum, a mass attached to a spring, and a vibrating guitar string. Other examples include the motion of a child on a swing, the motion of a diving board, and the motion of a car's suspension system on a bumpy road.

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