# Simple harmonic motion equation

• Taylan
In summary: T##In summary, the problem is to calculate the harmonic motion equation for a given case with A = 0.1m, t = 0s, x = 0.05m, v(t=0) > 0, and a(t=0) = -0.8m/s^2. The equation for harmonic motion is x(t) = +/- Acos/sin((2pi/T)*t), where A is the amplitude of the motion, t is time, and T is the period. To determine the direction and sign of the graph, the velocity at t = 0 must be considered, which in this case is positive, resulting in a positive sign. However, since
Taylan

## Homework Statement

Calculate the harmonic motion equation for the following case
A=0.1m, t=0s x=0.05m, v(t=0)>0 a(t=0)= -0.8m/s^2

## Homework Equations

x(t)= +/-Acos/sin ( (2pi/T)/*t)

## The Attempt at a Solution

[/B]
A is given to be 0.1 so I simply place it into the equation. Now I have to decide whether the graph is sin or cos and the sign. Since the velocity is positive at t=0, the sign must be +. I am confused about whether it is sin or cos because the graph when I sketch it looks like a kind of transformation starting from t=0 x=0.05m and going upwards. I am also not sure about how to find T. is there an equation I am missing?

Taylan said:

## Homework Statement

Calculate the harmonic motion equation for the following case
A=0.1m, t=0s x=0.05m, v(t=0)>0 a(t=0)= -0.8m/s^2

## Homework Equations

x(t)= +/-Acos/sin ( (2pi/T)/*t)

## The Attempt at a Solution

[/B]
A is given to be 0.1 so I simply place it into the equation. Now I have to decide whether the graph is sin or cos and the sign. Since the velocity is positive at t=0, the sign must be +. I am confused about whether it is sin or cos because the graph when I sketch it looks like a kind of transformation starting from t=0 x=0.05m and going upwards. I am also not sure about how to find T. is there an equation I am missing?

If the motion at ##t=0## is neither at ##x=0## nor ##x = \pm A##, then the motion needs a phase angle.

Delta2
PeroK said:
If the motion at ##t=0## is neither at ##x=0## nor ##x = \pm A##, then the motion needs a phase angle.

Thank you! So:

0.1cos[(2pi/T)*0 + phi) = 0.05

phi= pi/3

What I end up with is:

x(t) = 0.1cos[(2pi/T)*t+pi/3)

Can please you give me further tips to find out the value of T?

if you find ##x(t)## then the equation for acceleration is ##a(t)=-\omega^2x(t)## and because it is given ##a(t=0)=-0.8## you ll have the following equation
##a(0)=-0.8=-\omega^2x(0)## with only unknown the ##\omega=\frac{2\pi}{T}##

Taylan

## What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth around a central equilibrium point, with a restoring force that is directly proportional to the displacement from the equilibrium point. Examples of simple harmonic motion include the motion of a pendulum and a mass on a spring.

## What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x(t) = A*cos(ωt + φ), where x(t) is the displacement from the equilibrium point at time t, A is the amplitude of the motion, ω is the angular frequency, and φ is the phase constant. This equation describes the position of the object at any given time during its motion.

## What are the units for the variables in the simple harmonic motion equation?

The units for the variables in the simple harmonic motion equation are as follows: x(t) and A are measured in meters (m), ω is measured in radians per second (rad/s), and φ is dimensionless (unitless).

## How is the period of simple harmonic motion related to the angular frequency?

The period (T) of simple harmonic motion is equal to 2π divided by the angular frequency (ω). In other words, T = 2π/ω. This means that as the angular frequency increases, the period decreases and the object completes more cycles of motion per unit time.

## What factors can affect the amplitude of simple harmonic motion?

The amplitude of simple harmonic motion can be affected by the initial conditions of the motion (such as the initial displacement and velocity), the mass of the object, and any external forces acting on the object. In addition, damping from friction or air resistance can also decrease the amplitude of the motion over time.

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