The graph below shows position as a function of time for a mass attached to a spring undergoing simple harmonic motion. Based on the information provided in the picture, determine the initial phase constant of this motion. Provide your answer in radians as a number between (-1.57) and (+1.57). Use 3 significant figures.
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2. a. The graph shows a position vs time graph for a mass oscillating on a spring. Estimate the phase constant ϕ. Replace this value into the expression x = A cos (ωt + ϕ) and show that the equation is consistent with the graph. Be careful about signs! b. At what position(s) is the potential energy (U) of a mass on a spring undergoing simple harmonic motion equal to 1/3 the kinetic energy (K) stored in the spring? Write your answer in terms of the amplitude A. Hint: Use the conservation of mechanical energy, that is, K + U = E for all points of the oscillation.
Frank D.
The equation that describes the location of a mass oscillating on a spring as a function of time is given by y(t) = A*sin(2πTt - π/2), where A is the amplitude, T is the period of oscillation, and t is the time. Suppose the period of oscillation is 3 seconds and the amplitude is 5 cm. Use your calculator to compute where the mass would be at a time t = 1.2 s relative to the equilibrium position x = 0 cm. Make sure the angles in your calculator are set to radians. -4.05 cm 0.082 cm 0.36 cm 4.05 cm
A mass oscillates on a spring with a period $T$ and an amplitude $0.48 \mathrm{cm} .$ The mass is at the equilibrium position $x=0$ at $t=0,$ and is moving in the positive direction. Where is the mass at the times (a) $t=T / 8$ (b) $t=T / 4$ (c) $t=T / 2$ and (d) $t=3 T / 4 ?$ (e) Plot your results for parts (a) through (d) with the vertical axis representing position and the horizontal axis representing time.
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