Question

For the simple harmonic motion equation d = 5sin([2pi]t), what is the maximum displacement from the equilibrium position?

Answer 1

An SHM is displacement of particle about a mean position given by a general equation:
\[y=A \sin \omega t\] or \[y=A \cos \omega t\] where A is the amplitude. Now, in an SHM, the particle moves about the mean position and can go upto a maximum of two extreme positions on either side of the mean position. The distances of these extreme positions is the amplitude A itself. Thus, maximum distance is A units.
Now use your equation to extract the amplitude and get the max distance.