A body makes angular simple harmonic motion of amplitude `pi//10rad` and time period `0.05s`. If the body is at a displacement `theta = pi//10 rad` at `t = 0`, write the equation giving angular displacement as a function of time.

Explanation

To find the equation giving angular displacement as a function of time for a body in angular simple harmonic motion, we can follow these steps:

### Step 1: Identify the given values
- Amplitude (A) = π/10 rad
- Time period (T) = 0.05 s
- Initial displacement (θ₀) = π/10 rad at t = 0

### Step 2: Calculate the angular frequency (ω)
The angular frequency (ω) is calculated using the formula:
\[ \omega = \frac{2\pi}{T} \]
Substituting the value of T:
\[ \omega = \frac{2\pi}{0.05} = 40\pi \text{ rad/s} \]

### Step 3: Write the equation for angular displacement
The general equation for angular displacement in simple harmonic motion is given by:
\[ \theta(t) = \theta_0 \cos(\omega t) \]
Where:
- θ(t) is the angular displacement at time t
- θ₀ is the initial displacement
- ω is the angular frequency

### Step 4: Substitute the known values into the equation
Substituting θ₀ = π/10 and ω = 40π into the equation:
\[ \theta(t) = \frac{\pi}{10} \cos(40\pi t) \]

### Final Answer
The equation giving angular displacement as a function of time is:
\[ \theta(t) = \frac{\pi}{10} \cos(40\pi t) \]

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