Final answer:
The phase difference between two simple harmonic motions (SHMs) with equal amplitudes is 0 radians.
Step-by-step explanation:
In order to find the phase difference between two simple harmonic motions (SHMs) with equal amplitudes, we need to consider the equation for the resultant SHM. The amplitude of the resultant SHM is given by AR = √(A₁² + A₂² + 2A₁A₂cosΔ), where A₁ and A₂ are the amplitudes of the individual SHMs and Δ is the phase difference between them.
If the amplitude of the resultant SHM is equal to the amplitude of the superimposing SHMs (A), then we can write the equation as A² = A² + A² + 2A²cosΔ. Simplifying this equation gives us A = AcosΔ. Dividing both sides of the equation by A gives us cosΔ = 1, which implies Δ = 0, since the cosine of 0 is 1.
Therefore, if the amplitude of the resultant SHM is equal to the amplitude of the superimposing SHMs, the phase difference between them is 0 radians.