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 ?
Answer & explanation
Correct answer: option 4
We have :
- y = aT sin \(\frac{2 \pi t}{T}\)
- y = a sin vt
- y = \(\frac{a}{T}\) sin \(\frac{t}{a}\)
- 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)