A block attached to an ideal horizontal spring oscillates along the x-axis. The positive direction is defined as "to the right." At the instant defined as t=0s, the block is at its farthest rightward position and is momentarily at rest.
Throughout the motion, the block is described analytically by a single trigonometric function of time whose argument includes a constant phase angle φ.
(a) Identify whether a cosine function or a sine function is the more convenient choice for expressing the block’s position x(t), given the stated initial condition. Give a brief verbal justification without performing any calculations.
(b) State the numerical value of the phase angle φ (in radians) that must appear inside the argument of the trigonometric function you selected in part (a) so that the mathematical expression reproduces the initial condition exactly.
(c) Explain in words how the chosen combination of function type and phase angle ensures that the position is a maximum at t=0s while the velocity is zero.