Given,
Mass,
Stiffness constant of spring,
The time period of the harmonic motion can be given by
Frequency,
7. A spring with a 100 g mass hanging from it is set into simple harmonic...
Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed by the equation of motion where m is the mass, c is the damping coefficient of the damper, k is the stiffness of the spring, F is the net force applied on the mass, and x is the displacement of the mass from its equilibrium point. In this problem, we focus on a mass-damper-spring system with m = 1 kg, c-4 kg/s, k-3 N/m,...
A mass of 377 g is attached to a spring and set into simple harmonic motion with a period of 0.286 s. If the total energy of the oscillating system is 6.54 ), determine the following. (a) maximum speed of the object m/s (b) force constant N/m (c) amplitude of the motion
A mass of 317 g is attached to a spring and set into simple harmonic motion with a period of 0.326 s. If the total energy of the oscillating system is 6.54 J, determine the following. (a) maximum speed of the object m/s (b) force constant N/m (c) amplitude of the motion m
A mass of 207 g is attached to a spring and set into simple harmonic motion with a period of 0.226 s. If the total energy of the oscillating system is 6.14 J, determine the following. (a) maximum speed of the object m/s (b) force constant N/m (c) amplitude of the motion
A mass of 397 g is attached to a spring and set into simple harmonic motion with a period of 0.246 s. If the total energy of the oscillating system is 5.94 J, determine the following. (a) maximum speed of the object 6.49 When is the total energy of the mass-spring system equal to the kinetic energy of the mass? m/s (b) force constant N/m (c) amplitude of the motion Additional Materials Reading
Simple Hanging Harmonic Oscillator Developed by K Roos In this set of exercises the student builds a computational model of a hanging mass-spring system that is constrained to move in 1D, using the simple Euler and the Euler-Cromer numerical schemes. The student is guided to discover, by using the model to produce graphs of the position, velocity and energy of the mass as a function of time, that the Euler algorithm does not conserve energy, and that for this simple...
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 ?/? . At the time ? = 0 ?, the mass is 2cm above its equilibrium position. The 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...
A 0.50 kg mass oscillates in simple harmonic motion on a spring with a spring constant of 210 N/m . Part A What is the period of the oscillation? Part B What is the frequency of the oscillation?
Exercise 11: Simple Harmonic Motion 1. A spring-mass system oscillates with a frequency of 10 Hz when the mass is equal to 0.50 kg. What is the stiffness of the spring? With the same spring, what would the mass need to be to double the frequency? 2. A pendulum swings with a period of 1.50 seconds when the acceleration due to gravity is equal to 9.80 m/s? What is the length of the pendulum? How would this period change if...
10. A 1.5 kg mass is attached to the end set into simple harmonic motion wit ned to the end of a horizontal spring of spring constant 60 N/m and a. What is the maximum potential energy of the system? b. What is the frequency of vibration? c. What is the period of vibration?