9. A spring-mass system exhibits free, undamped motion and its position x() is depicted graphically below, where x() is measured in feet and t is measured in seconds. Assume that the mass weighs 8 pounds. Note: The horizontal axis is t and the vertical axis is x(t). Remember that positions below the equilibrium position are considered to be positive. a) Express the motion of the mass in the form x(t) =c₁cos(wt) + c2sin(wt). Give exact values for all quantities. x(t) т ° B t b) What is the initial velocity of the mass? (Exact or a 1 decimal place value is allowed here) c) What is the exact value of k, the spring constant for the system?

Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.

Transient Orifice Flow: Water is discharged from a reservoir through a long pipe as shown. By neglecting the change in the level of the reservoir, the transient velocity of the water flowing from the pipe, vt), can be expressed as: - Reservoir v(t) V2gh = tanh V2gh) Pipe Where h is the height of the fluid in the 7- reservoir, L is the length of the pipe, g is the acceleration due to gravity, and t is the time elapsed from the beginning of the flow Transient Orifice Flow: Determine the helght of the fluid in the reservoir at time, t= 2.5 seconds, given that the velocity at the outfall, vt) = 3 m/s, the acceleration due to gravity, g = 9.81 m/s? and the length of the pipe to outfall, L= 1.5 meters. Reservoir v(t) V2gh = tanh 2L 2gh water Pipe Hint: Transform the equation to a function of form: fih) = 0 Solve MANUALLY using BISECTION AND REGULA-FALSI METHODS, starting at xn = 0.1, Kg =1, E = 0.001 and If(*new)l < E

Express the mathematical relationship between stress and strain in case of elastic material.