Question

For a 2DOF system, how many natural frequency (frequencies) does it have? How many vibration(s) could it possibly have?

Answer #1

Write down the formula relating frequencies fn for
higher natural modes of vibration to the fundamental mode frequency
f1

29a)A violin string is set in vibration at a frequency of 440Hz.
How many vibrations does it make while its sound travels 200m if
the temperature is 25C
29b)A wire with a linear mass density of 2.5x10^-3 kg/m is under
35N of tension. If the wire is plucked what is the frequency of the
wave on the wire if its wavelength is 2m

6. (a) Calculate the first three frequencies of axial vibration
of a bar fixed at one end.
(b) Derive the
orthogonality condition of natural modes
of vibration in axial
direction.
(c)
Discuss the modal analysis
method.
(d). Determine the
first two frequency by Rayleigh-ritz method,
assuming

The natural frequency of vibration of a person is found to be
5.2 Hz while standing on a horizontal floor. Assuming damping to be
negligible, determine the vertical displacement of the person at
time = 0.5s when the floor is subjected to a vertical harmonic
vibration of frequency 5.3 Hz and amplitude 0.009m. Assume the mass
of the person to be 73kg. Answer in m with 3 decimal places.

1) How does the amplitude of vibration affect the time period of
vibration for a spring-mass system?
a)The period decreases linearly as amplitude increases
b)Time period increases as the square root of the amplitude
c)No effect
d)Time period increases linearly with the amplitude
2)What will be the value of the spring constant, if a mass of
1.1 kg attached to a spring stretches it by 16 cm. Ignore the mass
of the spring and its original length.
3)What will be...

Write a general statement that describes how the frequency of
vibration of a standing wave relates to the number of segments of
the standing wave.

Two adjacent natural frequencies of an organ pipe are determined
to be 780 Hz and 884 Hz. (Assume the speed of sound is 343
m/s.)
(a) Calculate the fundamental frequency of this pipe.
Hz
(b) Calculate the length of this pipe.
m

How many degrees of freedom does a system have if there are N
particles that can move in 3 dimensions and each particle has a
spin that can point either up or down? How many total spin states
are available to this system?

How many subspaces does R1 have? How many subspaces does R2
have?

(A) How does a change in mass (for example, swapping a hydrogen
with a deuterium) affect the frequency of a molecular
vibration?
(B) How does a change in bonding strength (for example,
comparing a C-C single-bond to a C-C double bond) affect the
frequency of a molecular vibration?

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