Physics

Problem

For a particle executing SHM given by

x = A\cos(6 t + \phi)

, the initial displacement and velocity at

t = 0

are

x_0 = -0.04\,\text{m}

and

v_0 = -0.42\,\text{m s}^{-1}

. The initial phase

\phi

(expressed in degrees with

0^{\circ} \le \phi < 360^{\circ}

) is a)

300^{\circ}

60^{\circ}

120^{\circ}

240^{\circ}

Intuitive explanation

This problem asks you to find the initial phase by using the two initial conditions—position and velocity—as simultaneous constraints. At $t=0$ , substitute into both the displacement equation and its time derivative (velocity) to get two equations in two unknowns: $A$ and $\phi$ . The key insight is that $\cos(\phi)$ and $\sin(\phi)$ are related through the Pythagorean identity, so you can eliminate $A$ and solve for $\phi$ uniquely.

Intuitive explanation

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