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4Consider the spring-loaded pendalum system shown in Figure 4. Assume that the spring force acting on...
Question 5 Consider the spring loaded system shown below. Assume that the springs are undeformed when...
Question 5 Consider the spring loaded system shown below. Assume that the springs are undeformed when the pendulum is vertical (0-0). Assume the angle of oscillation θ is small. Derive the equation
1. What is a linear restoring force? 2. What type of force must be acting to...
1. What is a linear restoring force? 2. What type of force must be acting to produce simple harmonic motion? 3. If a pendulum is to undergo simple harmonic motion, should its displacement angle be large or small? 4. To what is the frequency of oscillation of a pendulum equal? 5. To what is the frequency of oscillation of a mass, m. suspended from a spring of mass, mis equal?
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two per...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
Consider the inverted pendulum system presented in Fig. 1. The pivot of the pendulum is mounted o...
Consider the inverted pendulum system presented in Fig. 1. The pivot of the pendulum is mounted on a cart, which can move in a horizontal direction. The pendulum can be kept balanced at a specific position by applying a horizontal force to drive the carriage. Assume that the pendulum mass, m, is concentrated ia at the end of the massless rod. The horizontal displacement of the pivot on the cart is x, the rotational angle of the pendulum is θ...
A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h bel...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h bel...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
4. Consider the pendulum with friction modeled by the second order ODE: where θ is the angle the ...
4. please help with both parts a and b
4. Consider the pendulum with friction modeled by the second order ODE: where θ is the angle the pendulum makes with the vertical axis, α is a friction coefficient and w is the pendulum natural frequency. (a) Turn (4) into a first order system. (b) Use Euler method to find an approximation to the solution in [0,5] with initial conditions θ(0)-1 and θ'(0)-0. Take α-0.2 and w-2. Verify the expected order...
An inverted pendulum system is shown in Figure 1. It is assumed that the pendulum is...
An inverted pendulum system is shown in Figure 1. It is assumed that the pendulum is a mass on a massless rod of length l-0.5 m and the mass on the tip of the rod, m1 kg. The mass of the cart M-5 kg. Assume also that there is no friction in the system The displacement of the cart is indicated by x and the displacement of the pendulum is shown as θ Figure 1. Inverted Pendulum on a cart...
Consider the mass-spring-damper system depicted in the figure below, where the input of the system is...
Consider the mass-spring-damper system depicted in the figure below, where the input of the system is the applied force F(t) and the output of the system is xít) that is the displacement of the mass according to the coordinate system defined in that figure. Assume that force F(t) is applied for t> 0 and the system is in static equilibrium before t=0 and z(t) is measured from the static equilibrium. b m F Also, the mass of the block, the...
Please be as detailed as possible cause I want to understand it. Thanks! 14 Figure 1:...
Please be as detailed as possible cause I want to understand it.
Thanks!
14 Figure 1: Sliding pendulum 4. (38pt) Practice power expansion and initial condition A block of mass M is free to slide on a horizontal bar without any friction. A mass m is attached to the bottom of the block with a massless rod of length 1 and can oscillate freely in the same plane as the horizontal bar. (a) (5pt) Write down the Lagrangian of the...
Question 5 Consider the spring loaded system shown below. Assume that the springs are undeformed when the pendulum is vertical (0-0). Assume the angle of oscillation θ is small. Derive the equation
1. What is a linear restoring force? 2. What type of force must be acting to produce simple harmonic motion? 3. If a pendulum is to undergo simple harmonic motion, should its displacement angle be large or small? 4. To what is the frequency of oscillation of a pendulum equal? 5. To what is the frequency of oscillation of a mass, m. suspended from a spring of mass, mis equal?
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
Consider the inverted pendulum system presented in Fig. 1. The pivot of the pendulum is mounted on a cart, which can move in a horizontal direction. The pendulum can be kept balanced at a specific position by applying a horizontal force to drive the carriage. Assume that the pendulum mass, m, is concentrated ia at the end of the massless rod. The horizontal displacement of the pivot on the cart is x, the rotational angle of the pendulum is θ...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
4. please help with both parts a and b
4. Consider the pendulum with friction modeled by the second order ODE: where θ is the angle the pendulum makes with the vertical axis, α is a friction coefficient and w is the pendulum natural frequency. (a) Turn (4) into a first order system. (b) Use Euler method to find an approximation to the solution in [0,5] with initial conditions θ(0)-1 and θ'(0)-0. Take α-0.2 and w-2. Verify the expected order...
An inverted pendulum system is shown in Figure 1. It is assumed that the pendulum is a mass on a massless rod of length l-0.5 m and the mass on the tip of the rod, m1 kg. The mass of the cart M-5 kg. Assume also that there is no friction in the system The displacement of the cart is indicated by x and the displacement of the pendulum is shown as θ Figure 1. Inverted Pendulum on a cart...
Consider the mass-spring-damper system depicted in the figure below, where the input of the system is the applied force F(t) and the output of the system is xít) that is the displacement of the mass according to the coordinate system defined in that figure. Assume that force F(t) is applied for t> 0 and the system is in static equilibrium before t=0 and z(t) is measured from the static equilibrium. b m F Also, the mass of the block, the...
Please be as detailed as possible cause I want to understand it.
Thanks!
14 Figure 1: Sliding pendulum 4. (38pt) Practice power expansion and initial condition A block of mass M is free to slide on a horizontal bar without any friction. A mass m is attached to the bottom of the block with a massless rod of length 1 and can oscillate freely in the same plane as the horizontal bar. (a) (5pt) Write down the Lagrangian of the...
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