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# The black graph pictured below represents the position-time graph for a spring-mass system oscillating with simple harmonic motion. The coloured, 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 the graphs.Which coloured graph best represents the position 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 coloured graphs are equally possible

Last updated date: 29th May 2024
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Hint: We should know that velocity is defined as the rate change of displacement per unit time. Speed in a specific direction is also known as velocity. Velocity is equal to displacement divided by time. Speed, being a scalar quantity, is the rate at which an object covers distance. The average speed is the distance which is a scalar quantity per time ratio. On the other hand, velocity is a vector quantity; it is direction-aware. An object which moves in the negative direction has a negative velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion in this case. Based on this we have to solve this question.

It is known that for the spring mass system, an SHM, the position of mass is given by $x=A\sin (\omega t+\phi )$.
Now the velocity of the mass would be $v=\dfrac{dx}{dt}=A\omega \cos (\omega t+\phi )$.
Hence the function representing them must be ${{90}^{o}}$out of phase. Only the green curve can represent the velocity-time graph.