# Trouble with equations used in SHM calculations

• vf_one
In summary: Make sure to set your calculator to radians and include the negative sign in front of X when using these equations.
vf_one
Hi everyone

I'm having trouble using the equations for SHM calculations. We got told to set them on radians but I forgot to when I was doing the problems and got some of the answers right. But when I tried to do them when the calculator was set in radians, the answers were totally wrong.

We are given a set of equations to use

x=Xcos(2πft)
v= -X√(k/m)sin(2πft)
a= -XK/mcos(2πft)

Do we set the calculator to radians when we use these equations?
Do we take into account the negative "-" sign in front of X for the velocity and acceleration equations?

I'll show you the working a question I did and maybe you can see where I went wrong.

## Homework Statement

A 64kg bungy jumper is displaced 13m from equilibrium downwards and then released. She bounces up and down with a period of 5.4s. When she is 5m abover her initial rest position and moving upwards, what is her velocity?

2. The attempt at a solution

I calculated this with my calculator set in degrees
x=Xcos(2πft)
5=13cos(2π x 1/5.4t)
t= 57.9s

v= -X√(k/m)sin(2πft)
v= -13√(86.6/64)sin(2π x 1/5.4 x 57.9)
v= -14m/s

The answer was 14m/s. Why was the negative sign ignored?

But when we were asked to calculate the acceleration at 5m displacement the answer is
-6.77m/s2

a= -XK/mcos(2πft)
a= -13 x 86.6/64cos(2π x 1/5.4 x 57.9)
a= -6.77m/s2 Calculator still set in degrees

If anyone could help that would be very appreciated. Thanks

in advance!Yes, you should set the calculator to radians when you use those equations. The negative sign in front of X for the velocity and acceleration equations is taken into account. In your calculation for velocity, it looks like the negative sign was ignored which is why you got the wrong answer. For the acceleration, the negative sign was taken into account since the correct answer is -6.77m/s2.

## 1. What is SHM and why is it important?

SHM stands for Simple Harmonic Motion, which is a type of periodic motion where an object oscillates back and forth around a central equilibrium point. It is important because it is a fundamental concept in physics and is used to model many real-world phenomena, such as the motion of a pendulum or a mass on a spring.

## 2. How do I determine the period of an object in SHM?

The period of an object in SHM is the time it takes for one complete oscillation. It can be determined using the equation T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant. Alternatively, if given the frequency (f) of the oscillation, the period can be calculated as T = 1/f.

## 3. What is the equation for calculating the displacement of an object in SHM?

The equation for displacement in SHM is x = A cos(ωt), where x is the displacement, A is the amplitude (maximum displacement from equilibrium), ω is the angular frequency (2πf), and t is the time.

## 4. Can SHM equations be applied to real-world situations?

Yes, SHM equations can be applied to many real-world situations. For example, the motion of a car's suspension system can be modeled using SHM equations. However, it is important to note that these equations are simplified and may not perfectly represent the complex motion of real objects.

## 5. How do I account for damping in SHM calculations?

Damping is the decrease in amplitude of an oscillation over time due to external factors, such as friction. To account for damping in SHM calculations, a damping factor (b) can be added to the displacement equation: x = A e^(-bt/m) cos(ωt). The value of b will depend on the specific system and can be determined experimentally.

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