Equation of SHM is `x = 10 sin 10 pi t`. Then the time period is, x is in cm and t is in sec

Options

A. `10pi`
B. 0.2 sec
C. 0.1 sec
D. 2 sec

Answer

To find the time period of the simple harmonic motion (SHM) given by the equation \( x = 10 \sin(10 \pi t) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Standard Form of SHM**:
The standard equation of SHM is given by:
\[ x = A \sin(\omega t) \]
where \( A \) is the amplitude and \( \omega \) is the angular frequency.

2. **Compare with the Given Equation**:
From the given equation \( x = 10 \sin(10 \pi t) \), we can identify:
- Amplitude \( A = 10 \) cm
- Angular frequency \( \omega = 10 \pi \) rad/s

3. **Use the Formula for Time Period**:
The time period \( T \) of SHM is related to the angular frequency \( \omega \) by the formula:
\[ T = \frac{2\pi}{\omega} \]

4. **Substitute the Value of \( \omega \)**:
Now, substituting \( \omega = 10 \pi \) into the formula:
\[ T = \frac{2\pi}{10\pi} \]

5. **Simplify the Expression**:
The \( \pi \) in the numerator and denominator cancels out:
\[ T = \frac{2}{10} = \frac{1}{5} \]

6. **Convert to Decimal**:
Converting \( \frac{1}{5} \) to decimal gives:
\[ T = 0.2 \text{ seconds} \]

### Final Answer:
The time period \( T \) is \( 0.2 \) seconds.

---