A 100 N force deflects a spring by 0.05 m. A.)What is the value of the spring co
ID: 1795920 • Letter: A
Question
A 100 N force deflects a spring by 0.05 m. A.)What is the value of the spring constant? B.) What is the natural frequency, f, of vibration of a 50 kg mass attached to this spring and allowed to vibrate?
Write the equation of motion, x(t), for the spring/mass system in Problem #1, if the maximum deflection of the vibrating mass is 4 cm, and the position of the mass at t=0 sec is x = -2 cm.
In the previous problem, calculate the magnitude and direction of the velocity of the mass at t = 0 sec.
In the previous problem, calculate the position of the mass at t = 0.3 sec.
Prove whether or not the function x(t) = 10 sin (20t + /4) is a solution to the differential equation for simple harmonic motion. Show all work, or no credit!
Through how many cycles will a pendulum swing in 28 seconds, if a 6 kg mass is attached to a 1.00 m long string? What is the period of vibration?
For the pendulum in Problem #6, calculate the angular frequency, w, of the vibration if the pendulum is used on Mars (acceleration due to gravity is 3.75 m/s2 ).
On the Earth, a simple pendulum has a period of 4 sec. What is the period of this same pendulum on the surface of Mars, where gM = 3.75 m/s2?
Prove whether or not the function y(x,t) = 6(4x – 20t)2 is a solution to the differential wave equation. If it IS a solution, then determine the wave velocity.
When a piano tuner named Opperknockity stretches a 1.2 m long steel piano wire with a tension of 800 N, the velocity of a wave propagated along the string is 400 m/s. A) Calculate the mass per unit length, µ, of the wire. B) What would be the frequency of the fundamental mode of vibration of this string? C) How many times will Mr. Opperknockity tune this particular piano string?
Calculate the frequency of an FM radio wave of wavelength 2.956 meters. Assume that the speed of light is 3 x 108 m/s.
Consider a long hollow pipe closed at one end. Sketch the 3rd and 5th harmonics that could be supported in this air column. Calculate the frequency and wavelength of the FIFTH harmonic, given that the speed of sound in air is 340 m/s and the tube length is 60 cm.
Consider a standing wave on a string of length L = 0.6 m. Both ends are fixed. Sketch the following two harmonics.
Two guitar strings are plucked simultaneously. One string vibrates at 230 Hz while the other one vibrates at 234 Hz. What is the beat frequency of the resulting sound?
A 2nd Harmonic standing wave with amplitude of 4 mm exists on a 0.5 m long string that is fixed at both ends. The wave velocity for this string is 200 m/s. Using the wave function for a standing wave, y(x,t) = A sin(kx) sin(wt), calculate the vibration amplitude at x = 0.15 m, when t = 1.2 s.
In the previous problem, how far away from this speaker would the average person have to be before they could no longer hear the speaker??? (Assume there are no other interfering sources of sound).
A speaker emits a sound wave having 50 Watts of power. Calculate the sound intensity in W/m2 at a distance of 10 meters away from the speaker.
In the previous problem, calculate the difference in intensity levels, in deciBels, of the intensity at 25 m compared to the intensity at 10 m away from the speaker.
What is the relative intensity level in decibels if you were to A) DOUBLE the sound intensity level of a 0.001 W/m2 sound, and B) QUADRUPLE the sound intensity level of a 0.001 W/m2 sound?
A police siren is blaring out a constant 400 Hz tone as it is approaching you from behind at a rate of 30 m/s. You happen to be riding your bicycle at the rate of 10 m/s in the same direction as the police car. What frequency will you hear while you are ahead of the police car? What will be the CHANGE in frequency as it passes you and continues on ahead?
You want to build your own fife out of a piece of bamboo. With all the fingers holes closed, you want to produce a note with frequency 220 Hz (this is A below middle C on a piano). Assuming that the air temperature is 20 C, how long should you make the fife?
Calculate the resultant amplitude at the position x = 0.25 m at t = 0.8 sec of two waves simultaneously traveling along the length of the string. The equations of motion of the waves are y1(x,t) = 4 [mm] sin (2x – 0.5t) and y2 (x,t) = -6 [mm] cos (2x + 0.5t).
A traveling wave propagating down a long string has an equation of motion given by
y(x,t) = 4 sin ( x/3 + 400t) [cm].
Calculate the a) Amplitude b) frequency c) wavelength d) angular frequency e) wave constant f) wave speed
Explanation / Answer
Solving 1st question
Spring constant=F/x=2000 N/m
Natural frequency=sqrt(K/m)/2pi=1.006 Hz
Equation of motion
x=4sin(6.32t+b)
at t=0,x=-2 so b=-30 degree
x=4sin(6.32t-30)
velocity=dx/dt=25.28cos(6.32t-30)
at t=0,v=21.9 m/s
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