3.2.4 Worked example 3.1
Module 3: Waves
In this worked example we will show that the general solution x(t)=A⋅sin(ωt+ϕ) for a mass spring system is a solution to the differential equation that follows from the force balance, which is given by:
This solution is also referred to as the equation of motion of a harmonic oscillator.
In the equation of motion:
- x is the position of the mass with respect to the equilibrium position.
- A is the amplitude of the sinusoid, which is the maximum deviation from the equilibrium position.
- ω is the angular frequency at which the mass oscillates.
- ϕ is the phase deviation, which causes a nonzero starting point.
This worked example provides a framework to show that the equation of motion presented above is indeed a solution to the differential equation for the harmonic oscillator and to determine under which condition this is true.
In this exercise, you can write ω as omega and ϕ as phi.
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