A student organization has 12 members. A committee of 5members needs to be selected. How many ways can the committee be formed?

A fair coin is flipped 10 times. What is the probability that the coin lands on heads exactly 6 times?

A machine produces screws, and each screw has a 10% chance of being defective. A customer orders a batch of 25 screws. What is the probability that no more than 2 screws are defective in the batch?

Q29

1. Consider a pendulum consisting of two point masses on a single rod as shown below. The external torque acting on the pendulum is u(t). Suppose, the damping coefficient of the frictional toque is b. Find the nonlinear differential equation for the pendulum angle 0. m

4. Consider the following fluid system consisting of two tanks. Bult) Assume, R = 10, p = 1, g = 10 and ẞ = 1. a) Find the differential equation of the system. b) Find the transfer function (s) U(s)

Q13

3. Consider the following thermal system with two objects. Assume both objects have the same thermal capacity C and the thermal resistance of the separating conductor is R. Suppose the heat flow to the left object is u(t) Joule/s. a) Find the differential equation model of the system. T₂(s) b) Find the transfer function U(s)* T1 Τε N

2. Consider the DC motor differential equation derived in the class. Suppose we are driving the motor with constant input ū. a) Find the expression for steady-state angular speed of the motor in terms of ū and motor parameters J, L, R, K, Ka and b. di dw = Note that in steady state, 0. dt dt b) Looking at the expression you have for speed of the motor, suggest a parameter that you should change to increase the speed.