# Help with Simple Harmonic Motion

• cde42003
In summary: Then you can solve for A and omega.In summary, the conversation is about two physics problems. The first problem involves finding the angular frequency and amplitude of a block on a spring based on its position at two different times. The person is stuck because they need to know the period in order to find the frequency. The second problem is about determining the maximum frequency at which a penny can remain in place on a piston undergoing simple harmonic motion. The person is unsure how to relate the amplitude and frequency in order to solve the problem. They are advised to form a system of equations using the given data in order to find the missing variables.
cde42003
I need help on a couple of problems.

1. A block on a spring is pulled to the right and released at t= 0s. It passes x = 3.0 cm at t= 0.685s, and it passes x= -3.0 cm at t= 0.886s.

What is the angular frequency?

What is the amplitude?

I know what equatios I need to use, but without knowing what the period is I can't figure out how to find the frequency. Once I have the period, I know how to figure the rest out so that is where I am stuck.

2. A penny rides on top of a piston as it undergoes vertical simple harmonic motion with an amplitude of 4.0 cm. If the frequency is low, the penny rides up and down without difficulty. If the frequency is steadily increased, there comes a point at which the penny leaves the surface.

What is the maximum frequency for which the penny just barely remains in place for the full cycle?

On this question, I honestly have no idea how to solve it. I know I need to relate the amplitude and the frequency together in some fashion, but do not know how or what to use to do this.

Thanks

1)

Analyze both data given in the equation $x = A \cos \omega t$

2)

When the normal force = 0, the penny is not in contact with the surface.

Maybe I am missing something, but how can you use $x = A \cos \omega t$ when you do not know either A or omega?

cde42003 said:
Maybe I am missing something, but how can you use $x = A \cos \omega t$ when you do not know either A or omega?

You have x and t for 2 cases, so you can form a system of 2 equations.

## 1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction of the displacement.

## 2. What is the equation for Simple Harmonic Motion?

The equation for Simple Harmonic Motion is x(t) = Acos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase constant.

## 3. How is Simple Harmonic Motion different from other types of motion?

Simple Harmonic Motion is different from other types of motion because the restoring force is directly proportional to the displacement, resulting in a sinusoidal motion. Other types of motion may have more complex equations for the restoring force and displacement.

## 4. What are some real-life examples of Simple Harmonic Motion?

Some real-life examples of Simple Harmonic Motion include the motion of a pendulum, the vibrations of a guitar string, and the motion of a mass attached to a spring.

## 5. How is Simple Harmonic Motion related to Hooke's Law?

Simple Harmonic Motion is related to Hooke's Law because both describe the relationship between the restoring force and displacement. Hooke's Law states that the restoring force of a spring is directly proportional to the displacement from equilibrium, which is the same principle behind SHM.

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