For a simple harmonic oscillator, which of the following pairs of vector quantities always point in the same direction throughout the motion? (Note: the position vector defines the object's displacement from equilibrium.) Note: there are two correct answers restoring force and acceleration position and acceleration position and velocity velocity and acceleration

O Macmillan Learning A small bolt with a mass of 27.0 g sits on top of a piston. The piston is undergoing simple harmonic motion in the vertical direction with a frequency of 1.45 Hz. Use g = 9.81 m/s² for the acceleration due to gravity. What is the maximum amplitude Amax with which the piston can oscillate without the bolt losing contact with the piston's surface? Amax = m

What is true about the acceleration of a simple harmonic oscillator? (Choose all correct answers; there may be more than one correct answer.) O The acceleration is a maximum when the object is instantaneously at rest. O The acceleration is a maximum when the displacement of the object is a maximum. O The acceleration is a maximum when the speed of the object is a maximum. O The acceleration is zero when the speed of the object is a maximum. O The acceleration is a maximum when the displacement of the object is zero.

An object executes simple harmonic motion with an amplitude A. (Use any variable or symbol stated above as necessary.) (a) At what values of its position does its speed equal half its maximum speed? x = ±        (b) At what values of its position does its potential energy equal half the total energy? x = ±

When taking my pet turkey to the vet, the scale read a mass of 29 kg. The scale consists of a spring that has a force constant value of 36000 N/m.   Part (a)  What distance did the spring move when the pet turkey jumped onto the scale?  d=     m    Part (b)  Assuming that the spring behaves as a simple harmonic oscillator, what is the oscillation frequency of the spring when the pet turkey steps on the scale?  f =    Hz