Explore BrainMass
Share

Spring System Problem

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

1. A 2 kg block is attached to a spring and placed on a horizontal smooth surface. A horizontal force of 20 N is required to hold the block at rest when it is pulled 0.2 m from its equilibrium position. The block is released from its rest from this point, and is subsequently undergoes simple harmonic motion. Find a) the spring stiffness; b) the frequency of oscillations; c) the maximum speed of the block. Where does this maximum speed occur? Find the total energy of the oscillating system. Find the speed when the position equals one third of the maximum value.

Please see attached for the full question.

© BrainMass Inc. brainmass.com October 24, 2018, 6:23 pm ad1c9bdddf
https://brainmass.com/physics/resonance/spring-system-problem-39257

Attachments

Solution Preview

1.) a.)
Force F = 20 N
mass m = 2 kg
maximum displacement from the mean position x_max = 0.2 m

Because, F = k*x
=> stiffness constant k = F/x = 20/0.2 = 100 N/m --Answer

b.) Frequency of oscillation f = (1/2*pi)*sqrt(k/m) = (1/2*pi)*sqrt(100/2) = 1.125 Hz --Answer

c.) By energy law,
Total energy = potential energy at maximum displacement = maximum K.E. at 0 displacement from mean
(1/2)*k*x_max^2 = (1/2)*m*v_max^2
=> v_max = sqrt(k/m)*x_max = sqrt(100/2)*0.2 = 1.414 m/s ...

Solution Summary

This solution is provided in 376 words. It includes calculations for spring stiffness, and uses energy law to calculate total energy. Many other simple calculations are done, and an attached .jpg file is given with a diagram.

$2.19
See Also This Related BrainMass Solution

Physics Wave Problems

11. A particle in simply harmonic motion has a frequency of 40 Hz. What is the period of this oscillation?

17. (a) At what position is the speed of mass in a mass-spring system maximum? (1) x = 0, (2) x = -A, or (3) x = +A. Why? (b) If m = 0.250 kg, k = 100 N/m, and A = 0.10 m, what is the maximum speed?

33. The simple pendulum in a grandfather clock is 1.0 m long. What are (a) the period and (b) the frequency of this pendulum?

43. (a) If the spring constant in a mass-spring system is tripled, the new period is (1) 3, (2) square root of 3, (3) 1/square root of 3 times the old period. Why?

(b) If the initial period is 2.0 s and the spring constant is halved, what is the new period?

45. In a lab experiment, you are given a spring with a spring constant of 12 N/m. What mass would you suspend on the spring to have an oscillation period of 0.91 s when the mass is in SHM?

51. (a) If a grandfather clock were taken to the Moon, where the acceleration due to gravity is only one-sixth (assume the figure to be exact) that on the Earth, will the period of vibration (1) increase, (2) remain the same, or (3) decrease? Why? (b) If the period on the Earth is 2.0 s, what is the period on the Moon?

63. A longitudinal sound wave has a speed of 340 m/s in air. If this wave produces a tone with a frequency of 1000 Hz, what is its wavelength?

71. In watching a transverse wave go by, a woman in a boat notes that 13 crests pass by in a time of 3.0 s. If she measures the distance between two successive crests to be 0.75 m, and if the first and the last points that pass her are crests, what is the speed of the wave?

75. Fred strikes a train rail with a hammer at a frequency of 0.50 Hz, and Wilma puts her ear to the rail 1.0 km away. (a) How long after the first strike does Wilma hear the sound? (b) What is the time interval between the successive sound pulses she hears?

View Full Posting Details