Physics Q91 – AP-EAMCET 2026

In SHM, velocity leads displacement by

Clue 1 of 3: Phase Relationship in SHM

In Simple Harmonic Motion, different physical quantities like displacement, velocity, and acceleration oscillate with the same angular frequency but have different phase relationships.

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Step 1: Define Displacement in SHM✦ Active

The displacement of a particle undergoing Simple Harmonic Motion (SHM) can be represented by a sinusoidal function. A common form is:

x (t) = A \sin (ω t)

where $A$ is the amplitude, $ω$ is the angular frequency, and $t$ is time.

Step 2: Derive Velocity from Displacement○ Expand

Velocity ( $v$ ) is the time derivative of displacement ( $x$ ). Differentiating the displacement equation with respect to time, we get:

v (t) = \frac{d x}{d t} = \frac{d}{d t} (A \sin (ω t)) = A ω \cos (ω t)

💡 Teacher's Secret Hint

Remember that the derivative of $\sin (a t)$ is $a \cos (a t)$ and the derivative of $\cos (a t)$ is $- a \sin (a t)$ .

Step 3: Compare Phases of Velocity and Displacement○ Expand

To compare the phase of velocity with that of displacement, we need to express the velocity function in terms of a sine function. We use the trigonometric identity $\cos (θ) = \sin (θ + \frac{π}{2})$ or $\cos (θ) = \sin (θ + 90^{\circ})$ .

v (t) = A ω \cos (ω t) = A ω \sin (ω t + 90^{\circ})

Comparing the phase of $x (t) = A \sin (ω t)$ with $v (t) = A ω \sin (ω t + 90^{\circ})$ , we can see that the phase of velocity is $90^{\circ}$ greater than the phase of displacement. Therefore, velocity leads displacement by $90^{\circ}$ .

💡 Teacher's Secret Hint

A positive phase shift (e.g., $+ 90^{\circ}$ ) means the quantity 'leads' or occurs earlier in the cycle compared to the reference quantity.

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Physics Question 91 – AP-EAMCET 2026

Clue 1 of 3: Phase Relationship in SHM

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