A block in SHM starts from `+ A` position. Write `S - t` equation of the block, if `S` is measured from `-A`.

Options

A. `S = A(1 + cos omega t)`
B. `S =2 A(1 + cos omega t)`
C. `S = A(cos omega t)`
D. `S = A(1 + 2cos omega t)`

Explanation

To find the \( S - t \) equation of a block in Simple Harmonic Motion (SHM) that starts from the position \( +A \), with \( S \) measured from \( -A \), we can follow these steps:

### Step 1: Understand the Initial Position
The block starts at position \( +A \) at time \( t = 0 \). In SHM, the position \( x \) of the block can be described by the equation:
\[ x(t) = A \cos(\omega t) \]
where \( A \) is the amplitude and \( \omega \) is the angular frequency.

### Step 2: Define the New Reference Point
Since \( S \) is measured from \( -A \), we need to relate \( S \) to the position \( x \). The distance \( S \) from \( -A \) to the block's position \( x \) can be expressed as:
\[ S = x + A \]
This is because when the block is at \( -A \), \( S \) will be zero.

### Step 3: Substitute the Position Equation
Now, substitute the expression for \( x(t) \) into the equation for \( S \):
\[ S = (A \cos(\omega t)) + A \]

### Step 4: Simplify the Expression
Combine the terms:
\[ S = A + A \cos(\omega t) \]
Factoring out \( A \):
\[ S = A(1 + \cos(\omega t)) \]

### Final Equation
Thus, the equation relating \( S \) and \( t \) is:
\[ S(t) = A(1 + \cos(\omega t)) \]