Question
In: Mechanical Engineering
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.
Solutions
samet mamat answered 2 years agoRelated Solutions
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
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
A mass weighing 12lb stretches a spring 10in.. The mass is attached to a viscous damper...
A mass weighing 12lb stretches a spring 10in.. The mass is
attached to a viscous damper with damping constant 3lb*s/ft. The
mass is pushed upward, contracting the spring a distance of 2in,
and then set into motion with a downward velocity of 4in/s.
Determine the position of the mass at any time . Use as 32ft/s^2the
acceleration due to gravity. Pay close attention to the units.
A mass weighing 12lb stretches a spring 10in. The mass is attached to a viscous damper...
A mass weighing 12lb stretches a spring 10in. The mass is
attached to a viscous damper with damping constant 3lb⋅s/ft. The
mass is pushed upward, contracting the spring a distance of 2in,
and then set into motion with a downward velocity of 4in/s.
Determine the position u of the mass at any time t. Use 32ft/s2 as
the acceleration due to gravity. Pay close attention to the units.
u(t)=
A mass weighing 19lb stretches a spring 8in. The mass is attached to a viscous damper...
A mass weighing 19lb stretches a spring 8in. The mass is
attached to a viscous damper with damping constant 4lb⋅s/ft. The
mass is pushed upward, contracting the spring a distance of 2in,
and then set into motion with a downward velocity of 7in/s.
Determine the position u of the mass at any time t. Use 32ft/s2 as
the acceleration due to gravity. Pay close attention to the units.
Answer must be in inches
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...
1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring...
1.) A mass-spring system consists of an object of mass 1
Kilogram connected to a spring with a stiffness of 9. The damping
constant is 6. Derive the function (1) that determines the distance
from the equilibrium point if the initial position is 3 meters from
the equilibrium point and the initial speed is 3 meters per
second.
a.) What is the maximum distance from the equilibrium point?
b.) Determine the general solution of the nonhomogeneous linear
differential
equation using...
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
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