Question

Could you please answer all of the following questions?

1. A 3 kg object attached to a spring oscillates with an amplitude of 15 cm and a period of 2 s. At a time t = 0.5 s, the object's position is x = 9.1 cm. Determine

a) the spring constant of the spring

b) the total energy of the system (in joules)

c) the maximum speed of the object

d) the position of the object as a function of time. Use a cosine function

2. The velocity of a 300 g mass attached to the end of a spring is represented by v = (160 m/s)cos(2.83t + pi/4). Determine

a) the system's period of oscillation

b) the total energy of the system (in joules)

c) the acceleration of the mass as a function of time

3. A hollow sphere of radius 25 cm is attached to a piece of wire of length 10 cm to form a physical pendulum. Assuming small amplitude motion and ignoring the mass of the wire, determine its period of oscillation.  

4. A periodic wave is described by y = (0.15m)cos(10t + (pi/2)x) with x in meters and t in seconds. Determine

a) its wavelength

b) its speed

c) its direction of propagation

d) Sketch the wave at t = 0

Answer 1