5. A mass of 5 kg is attached to a spring with a spring constant k=20 N/m. The damping constant c=10 Ns/m provides resistance proportional to the velocity of the mass. The system is displaced 0.2 meters from equilibrium and released from rest. (a) Set up the differential equation that models the motion of the mass. (b) Solve the equation to find the displacement y(t) as a function of time. (c) What is the natural frequency and the actual oscillating frequency of this vibration system?

An astronaut has a mass of 68 kg. What is the weight of the astronaut on Earth at sea level? What are the mass and the weight of the astronaut on the Moon, and on Mars? What is the ratio of the pressure exerted by the astronauts shoe on Earth to Mars?

A structural member with a rectangular cross section as shown in the accompanying figure is used to support a load of 2500 N. What type of material do you recommend be used to carry the load safely? Base your calculations on the yield strength and a factor of safety of 2.0.

In Chapter 12, we explained that the electric power consumption of various electrical components can be determined using the following power formula: P = VI = RI2 where P is power in watts, V is the voltage, I is the current in amps, and R is the resistance of the component in ohms. Plot the power consumption of an electrical component with a resistance of 145 ohms. Vary the value of the current from zero to 4 amps. Discuss and plot the change in power consumption as the function of current drawn through the component.