Finding Parameters for Simple Harmonic Motion at t=1

• Jaimee
In summary, the problem involves finding the angular frequency, amplitude, and phase constant for a Simple Harmonic Motion (SHM) given the displacement, velocity, and acceleration at t=1s. The generic equation s=Acos(ωt+φ) is used to find the values of A, ω, and φ. The values of displacement, velocity, and acceleration at t=1s are used to solve for these variables.
Jaimee

Homework Statement

1. Consider a Simple Harmonic Motion
(SHM) for which, at time t = 1 s, the displacement is s=1 cm, the velocity is
2 cm s−1, and the acceleration is −3
cm s−2. Find the angular frequency, 4. amplitude, and phase constant for this motion.

Homework Equations

f=1/T
T=2pi*sqrt(m/k)=(2*pi)/w
w=v/R
v=-Awsin(wt)
s(t)=A*cos((2pi*t)/T)

The Attempt at a Solution

I have atached my attempt as a picture but I don't really know how to start

You are not asked or told about period, so don't bother with equations involving that.
Start with a generic form of equation, s=Acos(ωt+φ). You need the φ because phase is mentioned.
In terms of A, ω and φ, what are:
- the displacement when t=1,
- the velocity when t=1
- the acceleration when t=1?

What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium point under the influence of a restoring force that is directly proportional to the displacement from the equilibrium point.

What are the conditions for Simple Harmonic Motion?

The conditions for Simple Harmonic Motion are that the restoring force must be directly proportional to the displacement from the equilibrium point, and the motion must be periodic and repeat itself in a regular pattern.

What is the equation for Simple Harmonic Motion?

The equation for Simple Harmonic Motion is x(t) = A sin(ωt + φ), where x(t) is the displacement at time t, A is the amplitude (maximum displacement), ω is the angular frequency (related to the period of the motion), and φ is the phase angle (determines the starting point of the motion).

What is the relationship between Simple Harmonic Motion and a pendulum?

A pendulum is a classic example of Simple Harmonic Motion, as it swings back and forth under the influence of gravity. The restoring force is provided by the tension in the string, and the motion is periodic and follows the same equation as SHM.

What are some real-world examples of Simple Harmonic Motion?

Some real-world examples of Simple Harmonic Motion include the motion of a mass on a spring, the vibration of guitar strings, and the swinging of a pendulum. SHM can also be seen in the oscillations of sound waves and electromagnetic waves.

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