# Simple Harmonic Motion amplitude problem

• pondzo
In summary, the conversation discusses an object undergoing simple harmonic motion with a frequency of 3.1 Hz and an amplitude of 0.15 m. The question asks for the time it takes the object to go from x = 0.00 m to x = 7.00×10-2 m. The attempted solution uses the equation x(t)=Asin(ωt) and sets up an equation using the small angle approximation method. However, the solution is unable to be solved without the use of a graphics calculator. It is then suggested to use a simple scientific calculator and the inverse sine function to find the angle θ, which can then be used to solve the equation and find the correct answer of 2.49
pondzo

## Homework Statement

An object is undergoing simple harmonic motion with frequency f = 3.1 Hz and an amplitude of 0.15 m. At t = 0.00 s the object is at x = 0.00 m. How long does it take the object to go from x = 0.00 m to x = 7.00×10-2 m.

x(t)=Asin(ωt)

## The Attempt at a Solution

ω=2$\pi$f=6.2$\pi$
so, i set the following equation: 0.07=0.15sin(6.2$\pi$t)
but i can not solve it without the solving capabilities of a graphics calulator, so i can't use this method.

i then set up a similar equation using small angle approximation but in order to get it to the right accuracy i need to include the second term (ie sinθ=θ - θ3/6
but this then turns it into a cubic function (which i don't have the level of math to solve)

pondzo said:

## Homework Statement

An object is undergoing simple harmonic motion with frequency f = 3.1 Hz and an amplitude of 0.15 m. At t = 0.00 s the object is at x = 0.00 m. How long does it take the object to go from x = 0.00 m to x = 7.00×10-2 m.

x(t)=Asin(ωt)

## The Attempt at a Solution

ω=2$\pi$f=6.2$\pi$
so, i set the following equation: 0.07=0.15sin(6.2$\pi$t)
but i can not solve it without the solving capabilities of a graphics calulator, so i can't use this method.

You need a simple scientific calculator only. What is sin(6.2πt)? With inverse sine, (and setting the calculator to radian mode), get the angle θ=6.2πt.

ehild

Jerry Li and pondzo
Thank you for the quick reply ehild.

Wow, i can't believe i forgot about the inverse sine function on the normal calculators xD
thanks alot!

You are welcome

ehild

I would recommend using the equation x(t) = A cos(ωt + ϕ), where ϕ is the phase angle, to solve this problem instead of the small angle approximation. This equation accounts for the phase shift of the object's motion and will give you a more accurate solution. You can solve for the phase angle by setting x = 0 at t = 0 and then using the given values of x and t to solve for ϕ. Once you have the phase angle, you can use it to solve for the time it takes for the object to go from x = 0.00 m to x = 7.00×10-2 m. Alternatively, you can also use the equation v(t) = -Aωsin(ωt + ϕ) to find the time at which the object reaches its maximum displacement of 7.00×10-2 m. I hope this helps.

## 1. What is Simple Harmonic Motion (SHM)?

SHM is a type of periodic motion where a body moves back and forth around an equilibrium point due to a restoring force that is directly proportional to the displacement from the equilibrium point.

## 2. How is amplitude related to SHM?

Amplitude is the maximum displacement of a body from its equilibrium point during SHM. It determines the size or intensity of the oscillations and is directly proportional to the energy of the system.

## 3. How do you calculate the amplitude of an SHM problem?

The amplitude of an SHM problem can be calculated by finding the maximum displacement of the body from its equilibrium point. This can be done by observing the graph of displacement versus time or by using the equation A = xmax - xeq, where A is the amplitude, xmax is the maximum displacement, and xeq is the equilibrium point.

## 4. What factors affect the amplitude of an SHM problem?

The amplitude of an SHM problem is affected by the initial displacement of the body, the mass of the body, the spring constant, and the damping force (if present). These factors determine the energy of the system and thus, the amplitude of the oscillations.

## 5. How does the amplitude affect the period of an SHM problem?

The amplitude does not affect the period of an SHM problem. The period is solely determined by the mass of the body and the spring constant. However, a larger amplitude results in a greater distance traveled during each oscillation, which can affect the speed and acceleration of the body.

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