A book with printing error contains four different formulae for displacement. Choose the correct formula/formulae
(a) y = a sin 2 πt /T (b) y = a sin vt (c) y = a/ T sin ( t/ a ) (d) y = a/ T ( sin ( 2 π )t/ T + cos ( 2 π )t/ T )

Options

A. . y = a sin
2
π
T
t

2
π
T
t
B. y = a sin vt
C. y =
a
T
sin
(
t
a
)
D. y =
a
T
(
sin
(
2
π
)
T
t
+
cos
(
2
π
)
T
t
)

Explanation

To determine the correct formula for displacement from the given options, we need to analyze each formula based on the principles of dimensional analysis. The angle inside the sine function must be dimensionless.

### Step-by-Step Solution:

1. **Analyze Option (a)**:
\[ y = a \sin\left(\frac{2\pi t}{T}\right) \]
...