Question

For a particle performing linear SHM, its position (x) as a function of time (t) is given by x = Asin(ωt + δ). Given that, at t = 0, particle is at +A/2 and is moving towards x = +A. Find δ

• A. π/3 rad
• B. π/6 rad
• C. π/4 rad
• D. 5π/6 rad

Hint:

The phase constant δ in SHM depends on the initial conditions (position and ve locity at t=0). Carefully consider the sign of the sine and cosine of δ to find the correct value

Answer 1

The Correct Option is B

Step 1: Write the equation for \( \cos \theta \)

Using the given setup:

\[ \cos \theta = \frac{A}{2A} = \frac{1}{2} \]

Step 2: Solve for \( \theta \)

From the trigonometric identity:

\[ \theta = \frac{\pi}{3} \]

Step 3: Calculate the phase difference (\( \delta \))

The phase difference is given by:

\[ \delta = \frac{\pi}{2} - \frac{\pi}{3} \]

Simplify the expression:

\[ \delta = \frac{\pi}{6} \]

Final Answer:

The values are:

• \( \theta = \frac{\pi}{3} \)
• \( \delta = \frac{\pi}{6} \)