Question

The black graph pictured below represents the poition -time graph for a spring -mass system oscillating withnsimple harmonic motion.
The colored, dashed graphs represents 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

• 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

The correct option is C green

For a spring mass system(an SHM), the position of mass is given by

$x=Asin(\omega t+\varphi )$

The velocity of the mass would be $v=\frac{dx}{dt}=A\omega cos(\omega t+\varphi )$

Hence the functions representing them must be ${90}^{\circ }$ out of phase. Only the green curve can represent the velocity-time graph.