1. What is a simple harmonic oscillator? a) a system that satisfies a differential equation containing the 0th, 1st and 2nd derivatives of the displacement. b) a system exclusively acted on by a restoring force or torque that is proportional to the displacement.   c) a system that follows any type of periodic motion, like that described by a triangular function.   2.  What's true about the simple pendulum?   a) The restoring force is the tension force.   b) None of the other answers is correct.   c)The simple pendulum always behaves like a simple harmonic oscillator.   d) The angular frequency depends on the mass of the point mass attached to the string and the length of the string.

a) Compute the angular frequency and the spring constant    b) write the equation of motion x, v, and a for this oscillator.

2. A certain pendulum has a period of 1.60s on earth. What is the period of this pendulum on a planet that has gravitational acceleration of 3.71 m/s?

4. The displacement y(t) of an undamped oscillator of mass m>0 on a spring with spring constant k>0, and initial displacement a + 0 and initial velocity zero satisfies my" + ky = 0, y(0) = a, y'(0) = 0 %3D a. Solve this initial value problem. b. Show that the solution is periodic with period T, meaning that y(t+T)= y(t), and express Tin terms of m and k.

1. A pendulum with mass 2kg, length 2.5m swings with amplitude A = 2cm. After a long time the amplitude decreases to 1 cm due to air drag. How long is the period after the amplitude decrease? 2. What is the period of oscillation of the pendulum before and after the amplitude change?

1. If a spring has a spring constant of 23.0 N/m² then how much force is required to stretch it 11.0 cm from equilibrium? s Y91909 of a simple harmonic oscillator ever zero? If so, where?

Q3, first three parts

10. A block hangs on a spring attached to the ceiling and is pulled down 6 inches below itsequilibrium position. After release, the block makes one complete up-and-down cycle in 2seconds and follows simple harmonic motion. a. What is the period of the motion? b. What is the frequency? c. What is the amplitude? d. Write a function to model the displacement ? (in inches) as a function of the time ? (in seconds) after release. Assume that a displacement above the equilibrium point is positive.e. Find the displacement of the block and direction of movement at ? = 1 sec.

2. Dr. Benton has long thought that OSU should install a Foucault (simple) pendulum in the atrium of the Nobel Research Center. Let us consider how such a pendulum might function. Assume that the pendulum bob had a mass of 22 kg and was suspended from a thin 12 m long chord. Also, assume that the circular area over which the pendulum would swing was 4.9 m². Determine a) the period of the pendulum, and b) the maximum velocity of the pendulum bob.

1: In this question we will study the damped harmonic oscillator. Consider the following spring-mass system. kr bà Figure 1: Spring-mass system with a friction force. That is, an object of mass m is attached at the end of a spring with spring-constant k. We will also consider the effect of friction. Friction works in the opposite direction of motion, as illustrated in the figure. A) Show that the differential equation governing the damped spring-mass system is: më = -bå – kx (1) dr and i = dt where i = dt2 b) To solve the differential equation (1), we will take the following ansatz: r(t) = Ae. (2) If the above r(t) is a solution of Eq. (1) show that A has to satisfy the following equation: 1² +27d + wi = 0, (3) * and wi = k Solve the above equation to find A. m2 b where y 3= 2m c) For wi >?, show that the general solution can be written as: x(a) = Ae-t cos (wt +0) (4) where w? = w - 7². 2: Using Fermat's principle prove the law of reflection and the law of refraction of light.