Particle executing SHM along y-axis has its motion described by the equation `y=2 + 10 sin 5pi d`. Amplitude of SHM is

Options

A. 2
B. 12
C. 10
D. `sqrt104`

Answer

To find the amplitude of the simple harmonic motion (SHM) described by the equation \( y = 2 + 10 \sin(5\pi t) \), we can follow these steps:

### Step 1: Identify the general form of SHM
The general equation for SHM can be expressed as:
\[ y = A \sin(\omega t + \phi) + C \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( \phi \) is the phase constant,
- \( C \) is the vertical shift.

### Step 2: Compare the given equation with the general form
In our case, the given equation is:
\[ y = 2 + 10 \sin(5\pi t) \]
Here, we can identify:
- The vertical shift \( C = 2 \),
- The amplitude \( A = 10 \),
- The angular frequency \( \omega = 5\pi \).

### Step 3: Determine the amplitude
From the comparison, we see that the amplitude \( A \) is directly given by the coefficient of the sine function. Therefore, the amplitude of the SHM is:
\[ A = 10 \]

### Conclusion
The amplitude of the simple harmonic motion described by the equation \( y = 2 + 10 \sin(5\pi t) \) is **10 units**.

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