Consider the following pendulum that consists of a massless straight rigid rod aob with a point mass m attached at the bottom point a. the pendulum rotates without friction about the point o and it is initially at vertical equilibrium. a spring k is attached at the top point b and sets the pendulum to motion with the application of a vertical displacement input z(t). the spring k is unstretched at t = 0 and the pendulum is vertical. determine the linearized equation of motion of the pendulum about the vertical position

The heater element of a 120 v toaster is a 5.4 m length of nichrome wire, whose diameter is 0.48 mm. the resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10-6 ω·m. the toaster is operated at a voltage of 120 v. (a) what is the power drawn by the toaster? (b) if the cost of electricity is 12 ¢ per kilowatt-hour, and it takes 2 minutes to toast bread, how much does it cost for toasted bread? (c) when the heater element is at room temperature, is the resistivity in the nichrome wire greater than, less than, or equal to it’s resistivity when at operating temperature? explain.