System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Textbook Question
Chapter 1, Problem 1.14P
The displacement in meters of a certain vibrating mass is described by
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A tuning fork is struck, producing a pure
tone as its tines vibrate. The vibrations are modeled by the
function
v(t) = 0.7 sin(880t)
where u(t) is the displacement of the tines in millimeters at
time t seconds.
Find the frequency of the vibration, that is, the number
of times the fork vibrates per second.
The equation of motion of a particle in
simple harmonic motion is given by:
x(t) = 0.3cos(wt), where x is in meters
and t is in seconds. At x = 0, the
particle's velocity is v = -1.256 m/s. The
period of oscillation, T, equals:
O 1.5 sec
O 0.25 sec
O 0.5 sec
O 1 sec
O 3 sec
The equation of motion of a particle
in simple harmonic motion is given
by: x(t) = 0.1cos(wt), where x is in
meters and t is in seconds. At x = 0,
the particle's velocity is v = -1.256
m/s. The period of oscillation, T,
equals:
Chapter 1 Solutions
System Dynamics
Ch. 1 - Prob. 1.1PCh. 1 - Folklore has it that Sir Isaac Newton formulated...Ch. 1 - A ball is thrown a distance of 50 feet. 5 inches....Ch. 1 - An American football field is 100 yards long. How...Ch. 1 - How long is a 100-meter dash in feet?Ch. 1 - Convert 50 feet per second to miles per hour.Ch. 1 - The speed limit in some countries is 100...Ch. 1 - How many 60 watt lightbulbs are equivalent to one...Ch. 1 - Convert the temperature of 70°F to °C.Ch. 1 - Convert 30°C to °F.
Ch. 1 - A particular motor rotates at 3000 revolutions per...Ch. 1 - The displacement of a certain object is described...Ch. 1 - Prob. 1.13PCh. 1 - The displacement in meters of a certain vibrating...Ch. 1 - The distance a spring stretches from its “free...Ch. 1 - The following “small angle” approximation for the...Ch. 1 - Prob. 1.17PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Prob. 1.19PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Obtain a linear approximation of the function fh=h...Ch. 1 - The flow rate f in m3/s of water through a...Ch. 1 - Prob. 1.23PCh. 1 - The population data for a certain country are...Ch. 1 - Prob. 1.25PCh. 1 - Quenching is the process of immersing a hot metal...Ch. 1 - The useful life of a machine bearing depends on...Ch. 1 - 1.28 A certain electric circuit has a resistor and...Ch. 1 - 1.29 Water (of volume 425 ml) in a glass measuring...Ch. 1 - Consider the milk container of Example 1.4.2...Ch. 1 - Consider the milk container of Example 1.4.2...
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- In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, e"max, to the maximum angular velocity, e'max, is t s^(-1). What is the time needed for the pendulum to complete two oscillations? 1 sec 0.5 sec 2 sec 4 sec 0.25 sec A simple pendulum is set into motion at two different times with different inltlal conditions. The first time: the bob Is in its equilibrium position and is given an neriod of nmotion is T1 The second time: the bob is In its equilibrlum position and inm height reached by the bob is initial veloclty 2 m/s The maximum helght reached by the bob is ht.max and thearrow_forwardA 1.2 kg object is oscillating in simple harmonic motion at the end of an ideal horizontal spring ir the frictionless air track. Its position as a function of time t is given by r(t) = (0.045 m)cos[(15 rad/s)t - /8). a) What is the spring constant? k= N/m b) What are the frequency and period of the oscillation? f= Hz T= c) What is the maximum speed that the object reaches? vmax= m/s What is the particle's position when the velocity is maximum? d) What is the maximum acceleration that the object reaches? amax= m/s? What is the particle's position when the acceleration is maximum? e) What is the maximum energy of the system? KE= J f) Find the acceleration of the object when the object is at x=0.025 m. m/s2 a=arrow_forwardUse the proportionality constant for unit analysis where necessary.arrow_forward
- A simple pendulum is subjected to an initial excitation and oscillates in a frequency of 0.8 Hz. If the length of the pendulum is increased by 50%, find the new period of oscillation (in .sec)arrow_forwardmechanical vibration please answer this question belowarrow_forwardmechanical vibration answer the question belowarrow_forward
- 2 sec The equation of motion of a particle in simple harmonic motion is given by: x(t) = O.2cos(wt), where x is in meters and t is in seconds. At x = 0, the particle's velocity is v = -1.256 m/s. The period of oscillation, T, equals: O 1.5 sec O 0.5 sec O 1 sec 3 sec O 0.25 secarrow_forwardA tuning fork is struck, producing a pure tone as its tines vibrate. The vibrations are modeled by the function v(t) = 0.7 sin(880t) where v(t) is the displacement of the tines in millimeters at time t seconds. Find the period of the vibration.arrow_forwardSolve fast and accuratearrow_forward
- 1- Finding the values of the critical displacement (x) of the slide with different values of (theta) and drawing the relationship between (x) and (theta) theoretically and also finding the values of velocity and modulation theoretically with the change of angle (theta through equations (1, 2, 3) note:- r=25 mm, l=150 mm.arrow_forwardIn an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, 0"max, to the maximum angular velocity, O'max, is Tt s^(-1). What is the time needed for the pendulum to comnplete one-half oscillation? O 2 sec O 1 sec O4 sec 0.25 sec 0.5 sec Consider a place where the gravity is one-fourth the gravity on Earth (g = g/4), that placearrow_forwardOnly part a b and D thanksarrow_forward
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