A particle executing SHM along y-axis, which is described by `y = 10 "sin"(pi t)/(4)`, phase of particle at t =2s is

Options

A. `(pi)/(4)`
B. `(pi)/(2)`
C. `(pi)/(8)`
D. `pi`

Answer

To find the phase of a particle executing Simple Harmonic Motion (SHM) at a given time, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the SHM Equation**:
The equation of the particle in SHM is given as:
\[ y = 10 \sin\left(\frac{\pi t}{4}\right) \]
Here, the term inside the sine function, \(\frac{\pi t}{4}\), represents the phase of the particle.

2. **General Form of SHM**:
The general equation for SHM can be expressed as:
\[ y = A \sin(\omega t + \phi) \]
where \(A\) is the amplitude, \(\omega\) is the angular frequency, \(t\) is time, and \(\phi\) is the initial phase.

3. **Extract the Phase Expression**:
From the given equation, we can see that:
\[ \text{Phase} = \frac{\pi t}{4} \]

4. **Substitute the Given Time**:
We need to find the phase at \(t = 2\) seconds. Substitute \(t = 2\) into the phase expression:
\[ \text{Phase} = \frac{\pi \cdot 2}{4} \]

5. **Calculate the Phase**:
Simplifying the expression:
\[ \text{Phase} = \frac{2\pi}{4} = \frac{\pi}{2} \]

6. **Conclusion**:
Therefore, the phase of the particle at \(t = 2\) seconds is:
\[ \frac{\pi}{2} \]

### Final Answer:
The phase of the particle at \(t = 2\) seconds is \(\frac{\pi}{2}\).

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