Consider an underdamped spring-and-mass harmonic oscillator with a = 10 s¹ and y = 1 s-¹. Find the expressions for x(t) and sketch them graphically if a) att =0, x= 1 mand x = 0; b) at t = 0, x = 0 and x = 1 m/s.
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- Problem 1: A simple harmonic oscillator is composed of a mass hanging from a spring. The mass of the hanging object is 400 g and the spring constant is 0.8 2. At the time t = 0 s, the mass is 2cm above its equilibrium position. The т amplitude of the oscillation is 5 cm. a) What is the initial phase? b) Find one of the times where the mass is located at 3cm above equilibrium. c) Find the kinetic and potential energies at t = 1s. d) What is the maximum kinetic energy?Consider two pendulums with lengths l1 and l2 performing simple harmonic motion. Find theratio l1/l2, if it is given that the first pendulum swings back and forth 10 times per minute, and the second one swings back and forth 300 times per hour.A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any time is described by x = (7.7 cm) cos [2?t/(0.76 s)]. Determine the following. (Where applicable, indicate the direction with the sign of your answer. Assume the mass is initially stretched in the positive direction.) (a) period T of the motion s(b) location of the mass at t = 3.4 s cm(c) location of the mass at t = 3.4 s + T cm
- A mass of 7.2 kg is attached to a spring with the spring constant 30.0 N-m¹ and is placed on a frictionless surface with the spring attached to a wall. The spring is then compressed by 0.03 m and released to oscillate with simple harmonic motion. Calculate the absolute value of maximum velocity of the mass on spring. Provide your answer in Sl units.the spring constant? 3. The bicde of an electrie shaver moves back and forth with simple harmonic motion over a total distance of 2.2 mm and frequency 60. Hz. What is (a) the amplitude, (b) the maximum speed of the blade, and (c) the magnitude of the maximum acceleration of the blade?A mass on a spring is held at a distance of 0.05 m from the equalibrium position. It is then released at time t=0 and undergoes simple harmonic motion. If the mass was 0.2 kg and the spring constant k was 6 Nm-1, what is the velocity of the mass at time = 7 seconds?
- thin re is measured The second harmonic frequency for a long at 200 Hz when it is attached to the ceiling with amass in tied to its bottom. Adding an extra lkg to the hanging mass increases the second harmonic Frequency to 245 M₂. Findm [draw appropriate diagrams to explain]A simple harmonic oscillator consists of a 1.20 kg block attached to a spring. The block is ocillating back and forth along a straight line on a frictionless horizontal surface. A plot of the position of the block (in cm) as a function of time (in seconds) is shown below. What are (a) the spring constant of the spring and (b) the maximum speed and maximum acceleration of the block? (c) What is the velocity of the block at t = 1.50 s? 4. 3- 2- -2- -3- -4- -5+ 0.2 0.4 0.6 0.8 Position (cm)A 5.00 g particle oscillating in simple harmonic motion has its position given bythe equation: x(t) = (2.5 cm) cos (36.5 t) At what time is the particle at the 2.00 cm mark?