Question
In: Mechanical Engineering
Derive the equation of motion for the mass-spring damper system of the seismic instrument as shown...
Derive the equation of motion for the mass-spring damper system of the seismic instrument as shown in the Figure. If the mass is 2 kg the spring stiffness 2.35 kN/m. damping coefficient 10 N.sm and 1-40 cm, determine (a) the undamped natural frequency (b) the undamped natural period o Rundup (a) (d) the damped natural froquency (e) the damped natural period
Solutions
Expert Solution
Some parts of the question was not clear. I have gone ahead with assumptions. Hope this is fine.
Pl
get back for any query.
samet mamat answered 2 years agoRelated Solutions
A seismic instrument (a mass connected to a spring and a damper) is employed to record...
A seismic instrument (a mass connected to a spring and a damper)
is employed to record a periodic input signal y(t)=0.5cos(15?t),
where y = displacement [cm], t = time [sec]. The
damping ratio of the instrument is 0.6. Select a combination of
mass, spring constant, and damping coefficient to yield less than a
5% amplitude error in measuring the input signal.
The Equation of motion for the standard mass-spring-damper system is Mẍ + Bẋ + Kx =...
The Equation of motion for the standard mass-spring-damper
system is
Mẍ + Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},
determine the free response of the system to initial conditions {
x0 = -1m, v0 = 40 m/s}. To help verify the
correctness of your answer, a plot of x(t) should go through the
coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,
-0.2043}.
Numerically simulate the...
The Equation of motion for the standard mass-spring-damper system is Mẍ + Bẋ + Kx =...
The Equation of motion for the standard mass-spring-damper
system is
Mẍ + Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},
determine the free response of the system to initial conditions {
x0 = -1m, v0 = 40 m/s}. To help verify the
correctness of your answer, a plot of x(t) should go through the
coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,
-0.2043}.
Numerically simulate the...
The Equation of motion for the standard mass-spring-damper system is Mẍ + Bẋ + Kx =...
The Equation of motion for the standard mass-spring-damper
system is
Mẍ + Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},
determine the free response of the system to initial conditions {
x0 = -1m, v0 = 40 m/s}. To help verify the
correctness of your answer, a plot of x(t) should go through the
coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,
-0.2043}.
determine the steady-state...
Simulate the Spring Mass Damper System shown in Fig. Using MATLAB/Simulink, m being the mass of...
Simulate the Spring Mass Damper System shown in Fig. Using
MATLAB/Simulink, m being the mass of Vibrating System in Kg. c
Being the coefficient of damping in N-sec/m, K being spring
stiffness in N/m. For the values m=15kg C=100 N-sec/m k=200 N/m
mx''+cx'+kx=f0sinwt
For a basic spring-mass-damper system with the following information. Mass = 0.35kg Spring Constant = 10000...
For
a basic spring-mass-damper system with the following information.
Mass = 0.35kg
Spring Constant = 10000 N/m
Initial displacement = 10mm
Initial velocity = 0
Find the equations of motion both north displacement and
velocity with respect to time t for the damping ratios of 0, 0.1
and 1. Please show full working
1) Sinusoidal Motion Properties in Spring Mass System- A 200g mass hangs from vibrating spring at...
1) Sinusoidal Motion Properties in Spring Mass System- A 200g
mass hangs from vibrating spring at lowest point of 3cm above table
and at it's highest point at 12cm above table. It's oscillation
period is 4seconds. Determine the following:
a. The spring constant in terms of T (period)
b. The maximum velocity magnitude and maximum acceleration
magnitude
c. The velocity magnitude at 10cm above table
d. The vertical position, velocity magnitude and acceleration
magnitude at 5 seconds
How is the motion of the mass on the spring similar to the motion of the...
How is the motion of the mass on the spring similar to the
motion of the bob? How is it different? Then, why does the period
of a pendulum not depend on mass but it does for the spring?
Explain carefully. Simple harmonic motion is used to describe
physics most complex theories. How could something so simple
describe the most complex
The mass-spring-damper system has a 2 kg block is displaced by an amplitude of 50 mm...
The mass-spring-damper system has a 2 kg block is
displaced by an amplitude of 50 mm and
released. Ifthc phase angle ofrcsponse is 84.17o, how many cycles
(m) will be executed beforc
the amplitude is reduced to I mm. What are the undamped natural
frequency m« and spring
constant k ifthc period ofdamped oscillation rs is 0.3 scc.
Derive the equation of motion for the system and obtain its transfer function of Controller for...
Derive the equation of motion for the system and obtain its
transfer function of Controller for Propeller Driven
Pendulum showing the steps .
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