A student writes four different expressions for the displacement y in a periodic motion as a function of time t, a as amplitude, T as time period. Which of the following can be correct ?

y = \(\frac{a}{\sqrt{2}}\) [sin \(\frac{2 \pi t}{T}\) + cos \(\frac{2 \pi t}{T}\)]

We have : 

1. y = aT sin \(\frac{2 \pi t}{T}\)
2. y = a sin vt
3. y = \(\frac{a}{T}\) sin \(\frac{t}{a}\)
4. y = \(\frac{a}{\sqrt{2}}\) [sin \(\frac{2 \pi t}{T}\) + cos \(\frac{2 \pi t}{T}\)]

• In (1) and (3), the dimensions of RHS are NOT of displacement.
• In (2), the dimensions of the argument of sine are NOT dimensionless.

Thus, the answer is : (4)