# Hooke's Law: How to find Amplitude

• Absent.Crisis
In summary, the conversation is about a person studying Hooke's Law in Physics and struggling to understand the equation for Simple Harmonic Motion of a spring. They came across a reference book that explains the general solution for the differential equation, which includes the amplitude given by the square root of the sum of squared constants. The person then asks for clarification on what the constants represent and their physical meaning. Another person helps them understand by expanding the general solution and comparing it to the given form.
Absent.Crisis
Hello all,
(Newbie here so I hope I'm posting this in the right section, if not please guide me to the correct one)

I'm studying Hooke's Law in Physics and there is something I can't understand.
The equation for the Simple Harmonic Motion of a spring is given by $x'' + wx =0$

the general solution for the Differential equation above is given by: $A sin (wt) + B cos (wt)$

I came across a reference book that says: the amplitude is given by:
$sqrt {A^2 + B^2}$

I'd like to understand how they got this?? Right now I know that w is the angular frequency and wt gives the phase angle, but A and B as constants make no sense to me, what are they and what do they mean physically?

Last edited:
A more recognizable form of the general solution would be this:
$$A\cos (\omega t + \phi)$$
Where A is the amplitude. Expand this (using a trig identity) and compare with the form you were given.

Thanks a lot, I got it now :D

## What is Hooke's Law?

Hooke's Law is a physical law that describes the relationship between the force applied to an elastic material and the resulting deformation or change in length of the material.

## What is the formula for Hooke's Law?

The formula for Hooke's Law is F = -kx, where F is the force applied, k is the spring constant of the material, and x is the displacement or change in length of the material.

## How do you find the amplitude in Hooke's Law?

The amplitude in Hooke's Law is the maximum displacement or change in length of the material from its equilibrium position when a force is applied. To find the amplitude, measure the distance from the equilibrium position to the point of maximum displacement.

## What is the unit for the spring constant in Hooke's Law?

The unit for the spring constant in Hooke's Law is N/m (newton per meter). This unit represents the amount of force required to stretch or compress a material by one meter.

## Can Hooke's Law be applied to all materials?

Hooke's Law is typically only applicable to linear elastic materials, meaning that the relationship between force and displacement is directly proportional. Non-linear materials, such as rubber, may not follow Hooke's Law.

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