A 1.5-kg cart attached to an ideal spring with a spring constant ...

[PhilipSeeMore]

A 1.5-kg cart attached to an ideal spring with a spring constant of 20 N/m oscillates on a horizontal, frictionless track.
 
  At time t = 0.00 s, the cart is released from rest at position x = 10 cm from the equilibrium position.
  (a) What is the frequency of the oscillations of the cart?
  (b) Determine the maximum speed of the cart. Where does the maximum speed occur?
  (c) Find the maximum acceleration of the mass. Where does the maximum acceleration occur?
  (d) How much total energy does this oscillating system contain?
  (e) Express the displacement as a function of time using a cosine function.

Question 2

A thick slab of plastic lies at the bottom of a tank filled with water having an index of refraction of 1.33. A narrow laser beam is shone directly downward through the water on the plastic.
 
  You then gradually rotate the laser, thereby increasing the angle with respect to the normal that it strikes the plastic. You carefully note that at the instant the beam makes an angle of 66.5 with the normal in the water, no light enters the plastic, but it did enter for angles smaller than that. What is the speed of light in the plastic slab? (c = 3.00  108 m/s)

[tmlewis4706]

Answer to Question 1

(a) 0.58 Hz (b) 0.37 m/s, at the equilibrium position
(c) 1.3 m/s2, at maximum displacement (d) 0.10 J (e) x = (0.10 m) cos (3.7 s-1 t)

Answer to Question 2

2.46  108 m/s

[PhilipSeeMore]

TYSM

[laurnthompson]

Excellent