Which of the following statements is not true regarding a mass-spring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.

A spring hangs vertically from a ceiling. The spring constant of the spring is k=15 N/m. A 2kg object has been attached to the spring and the spring has already come to its new equilibrium. Someone pulls the object down by 5cm and releases it at time t = 0s. The spring and object begin to oscillate under simple harmonic motion. Find the total energy of the system, the maximum kinetic energy, the maximum potential energy, and the positions where the maximum energies occur.  Answers: 0.01875 J, 0.01875 J

A 0.50 kg object rests on a frictionless horizontal surface, where it is attached to a massless spring whose k-value equals 25.0 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The object is pushed, and the spring compressed, until  xi = −4.00 cm. It then is released from rest and undergoes simple harmonic motion. How fast is the object moving (in m/s) when the spring is momentarily compressed by 1.30 cm (that is, when x = −1.30 cm)?   How fast is the object moving (in m/s) whenever the spring is extended by 1.30 cm (that is, when passing through  x = +1.30 cm)?

A pendulum is undergoing simple harmonic motion. At a particular instant, you measure its speed to be v0,and you notice that exactly half of its energy is potential, and the other half is kinetic. It is a simple pendulum oflength l, with all of its mass (m) concentrated in a point at the end. a) In terms of v0, what is the highest speed the pendulum will reach?  b)What is the largest angle that the pendulum will reach?