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4. A pendulum is dropped at a given angle, θ. Derive an...
Derive the expression for the initial velocity v of a ballistic pendulum in terms of the...
Derive the expression for the initial velocity v of a ballistic pendulum in terms of the swept-out angle theta. Use the following equations of momentum and energy conservation... When the projectile and the pendulum stick together, they have total mass m + M and we define their combined velocity to be V⃗ . The relationship from conservation of momentum is: mv = (m + M)V⃗ Conservation of energy requires the initial kinetic energy of the pendulum system to equal the...
P4. A clock keeps time using the periodic motion of a simple pendulum. The pendulum consists...
P4. A clock keeps time using the periodic motion of a simple pendulum. The pendulum consists of a string of length L and a bob of mass m-5.00 kg attached to the end of the string. The pendulum has a period T-1.00 s. The initial angle (0) at 0 is equal to 0.175 rad. The bob is released from rest (i.e. -0) at -0. The angle between the string and the vertical is given by the equation: e-a cos (or...
(1 point) Suppose a pendulum of length L meters makes an angle of θ radians with the vertical, as n the figure t can be...
(1 point) Suppose a pendulum of length L meters makes an angle of θ radians with the vertical, as n the figure t can be shown that as a function of time, θ satisfies the differential equation d20 + sin θ-0, 9.8 m/s2 is the acceleration due to gravity For θ near zero we can use the linear approximation sine where g to get a linear di erential equa on d20 9 0 dt2 L Use the linear differential equation...
2. For the simple pendulum shown in Figure 2, the nonlinear equations of motion are given by θ(t)...
do (b) and (c) only.
2. For the simple pendulum shown in Figure 2, the nonlinear equations of motion are given by θ(t) + 믈 sin θ(t) + m 0(t)-0 Pivot point L, length Massless rod , mass Figure 2. A simple pendulum 3. Consider again the pendulum of Figure 2 of problem 2 when g = 9.8 m/s, 1 = 4.9m, k =0.3, and (a) Determine whether the system is stable by finding the characteristic equation obtained from setting...
Now damping is introduced and the angle θ is given by the equation: θ-ae" cos(or + φ). It is observed that after one hour the maximum angle of the pendulum has reduced to 0.122 rad due to the dam...
Now damping is introduced and the angle θ is given by the equation: θ-ae" cos(or + φ). It is observed that after one hour the maximum angle of the pendulum has reduced to 0.122 rad due to the damping force. e. (6) Calculate the coefficient α .
Now damping is introduced and the angle θ is given by the equation: θ-ae" cos(or + φ). It is observed that after one hour the maximum angle of the pendulum has reduced to...
show all steps please (1 point) Suppose a pendulum with length L (meters) has angle 0...
show all steps please
(1 point) Suppose a pendulum with length L (meters) has angle 0 (radians) from the vertical. It can be shown that 0 as a function of time satisfies the differential equation: d20 +sin0 0 dt2 where g 9.8 m/sec/sec is the acceleration due to gravity. For small values of 0 we can use the approximation sin(0)~0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length...
The angle of a pendulum is given by θ(t)=( 0.14 rad )cos( 4.0 t) , where...
The angle of a pendulum is given by θ(t)=( 0.14 rad )cos( 4.0 t) , where t is in seconds. A) Determine the amplitude. B)Determine the frequency. C)Determine the length of the string. D)Determine the angle at 1.0 s .
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...
[Q3-Lab/Home HL] Derive an algebraic expression that will relate the linear speed of the pendulum to...
[Q3-Lab/Home HL] Derive an algebraic expression that will relate the linear speed of the pendulum to the angle Q and du du do length L. Show work. [Hint: start from gsin(0) =gsin(0)] dt dᎾ dt
Please show all work and steps. Any help will be appreciated and thank you for your...
Please show all work and steps. Any help will be appreciated and
thank you for your time!
At a gathering with friends, you decide to play a game of regulation cornhole where the players attempt to throw a 1 lb bag filled with field corn through a 6-inch hole in a board located as shown in the diagram below. If the bag is released at a 30° angle and is airborne for 3 seconds, what is the velocity that the...
P4. A clock keeps time using the periodic motion of a simple pendulum. The pendulum consists of a string of length L and a bob of mass m-5.00 kg attached to the end of the string. The pendulum has a period T-1.00 s. The initial angle (0) at 0 is equal to 0.175 rad. The bob is released from rest (i.e. -0) at -0. The angle between the string and the vertical is given by the equation: e-a cos (or...
(1 point) Suppose a pendulum of length L meters makes an angle of θ radians with the vertical, as n the figure t can be shown that as a function of time, θ satisfies the differential equation d20 + sin θ-0, 9.8 m/s2 is the acceleration due to gravity For θ near zero we can use the linear approximation sine where g to get a linear di erential equa on d20 9 0 dt2 L Use the linear differential equation...
do (b) and (c) only.
2. For the simple pendulum shown in Figure 2, the nonlinear equations of motion are given by θ(t) + 믈 sin θ(t) + m 0(t)-0 Pivot point L, length Massless rod , mass Figure 2. A simple pendulum 3. Consider again the pendulum of Figure 2 of problem 2 when g = 9.8 m/s, 1 = 4.9m, k =0.3, and (a) Determine whether the system is stable by finding the characteristic equation obtained from setting...
Now damping is introduced and the angle θ is given by the equation: θ-ae" cos(or + φ). It is observed that after one hour the maximum angle of the pendulum has reduced to 0.122 rad due to the damping force. e. (6) Calculate the coefficient α .
Now damping is introduced and the angle θ is given by the equation: θ-ae" cos(or + φ). It is observed that after one hour the maximum angle of the pendulum has reduced to...
show all steps please
(1 point) Suppose a pendulum with length L (meters) has angle 0 (radians) from the vertical. It can be shown that 0 as a function of time satisfies the differential equation: d20 +sin0 0 dt2 where g 9.8 m/sec/sec is the acceleration due to gravity. For small values of 0 we can use the approximation sin(0)~0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length...
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...
[Q3-Lab/Home HL] Derive an algebraic expression that will relate the linear speed of the pendulum to the angle Q and du du do length L. Show work. [Hint: start from gsin(0) =gsin(0)] dt dᎾ dt
Please show all work and steps. Any help will be appreciated and
thank you for your time!
At a gathering with friends, you decide to play a game of regulation cornhole where the players attempt to throw a 1 lb bag filled with field corn through a 6-inch hole in a board located as shown in the diagram below. If the bag is released at a 30° angle and is airborne for 3 seconds, what is the velocity that the...
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