Question

The black graph pictured above represents the position-time graph for a spring-mass system oscillating with simple harmonic motion.
The colored, dashed graphs represent shapes of possible velocity time graphs for the same motion.
The vertical axis stands for position or velocity, but the scaling does not matter. The time axis is the same for all graphs.
Which colored graph best represents the possible velocity for the mass in this spring-mass system?

• A. Red
• B. Blue
• C. Green
• D. The velocity graph is the same as the position graph
• E. All three colored graphs are equally possible

Answer 1

Answer: (C)

Green

The given displacement graph of SHM represents the displacement $y$ as ,

$y=a\sin \omega t$ ,

where $a=$ amplitude ,

$\omega =$ angular frequency ,

therefore velocity ,

$v=dy/dt=a\omega \cos \omega t$

or $v=a\omega \sin (\omega t+\pi /2)$ ,

it is clear that velocity v is ahead of displacement by a phase angle of $\pi /2$ ,which is represented by green graph of velocity .