A mass spring system moves with simple harmonic motion along the x axis between turning points at , and . For parts (i) through (iii), choose from the same five possibilities. (i) At which position does the particle have the greatest magnitude of momentum? (a) 20 cm (b) 30 cm (c) 40 cm (d) some other position (e) The greatest value occurs at multiple points. (ii) At which position does the particle have greatest kinetic energy? (iii) At which position does the particle-spring system have the greatest total energy?
When an object undergoes simple harmonic motion, the position as a function of time may be written as
Position of object
At 40 cm we have the midpoint between the turning points, so it is the equilibrium position and the point of maximum speed, and therefore, maximum momentum. Option (c) is correct.
The position of maximum speed is also the position of maximum kinetic energy.
Option (c) is correct.
The total energy of the system is conserved, so it is the same at every position.
Option (e) is correct.
A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is determined. (i) When the elevator accelerates upward, is the period (a) greater, (b) smaller, or (c) unchanged? (ii) When the elevator has a downward acceleration, is the period (a) greater, (b) smaller, or (c) unchanged? (iii) When the elevator moves with constant upward velocity, is the period of the pendulum (a) greater, (b) smaller, or (c) unchanged?
A object attached to a spring moves without friction (b=0) and is driven by an external force given by the expression , where F is in Newton’s and t is in seconds. The force constant of the spring is . Find
(a) The resonance angular frequency of the system,
(b) The angular frequency of the driven system, and
(c) The amplitude of the motion.
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