How do these two equations explain how a simple pendulum is defined
as a point mass at the end of the length of negligable mass?Homework Answers
In both of these formulas,we take L as the length of pendulam,which basically means,distance between point of suspension of pendulam to centre of mass of the bob.If bob is not considered a point mass,we need to find its centre of mass and add it to the length of the rope.This makes our calculations and experiment more prone to errors.Hence simple pendulam's bob is considered as a point mass and length of the rope is taken as length of pendulam to avoid errors and we may focus on our experiment.
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How do these two equations explain how a simple pendulum is defined
as a point mass...
A simple pendulum is a massless string with a point mass at the end. The mass...
A simple pendulum is a massless string with a point mass at the end. The mass is 0.6 kg. The length of the pendulum is 0.1 m. The amplitude is 7.5°. What is the period of the pendulum?
8. A simple pendulum is a point mass on a massless string, and T, = 2「/,...
8. A simple pendulum is a point mass on a massless string, and T, = 2「/, A physical pendulum formed by a small mass on a lightweight string is approzimately a simple pendulum, but not quite, its period is T, 2n shorter than the period of a simple pendulum with the same length? Assume L is measured to the center of mass, and justify your answer. 2Vm L. Is the period of a physical pendulum longer or
A) Write the Lagrangian for a simple pendulum consisting of a point mass m suspended at...
A) Write the Lagrangian for a simple pendulum consisting of a point mass m suspended at the end of a massless string of length l. Derive the equation of motion from the Euler-Lagrange equation, and solve for the motion in the small angle approximation. B) Assume the massless string can stretch with a restoring force F = -k (r-r0), where r0 is the unstretched length. Write the new Lagrangian and find the equations of motion. C) Can you re-write the...
Prob. 7.3: A simple pendulum (mass M and length L) is suspended from a cart (mass...
Prob. 7.3: A simple pendulum (mass M and length L) is suspended from a cart (mass m) that canoscillate on the end of a spring of spring constant k, as shown in the figure at right. (a) Write the Lagrangian in terms of the generalized coordinates x and ?, where x is the extension of the spring from its equilibrium length and ? is the angle of the pendulum from the vertical. Find the two Lagrange equations. (b) Simplify the...
A simple pendulum has a rod of length LL with a bob of mass m=0.100 kg...
A simple pendulum has a rod of length LL with a bob of mass
m=0.100 kg at the end of the rod. The rod is supposed to be very
light and all the mass is imagined to be concentrated in the
bob.
A) What is the tension in the string when the pendulum swings by
an angle θ=5.00∘?
B) What is the magnitude of the restoring force on the bob when
θ=5.00∘?
C) If you drop a perpendicular from the...
A simple pendulum has a length L and a mass m. At its highest point, the...
A simple pendulum has a length L and a mass m. At its highest point, the pendulum mass is 0.25L above its lowest point (see figure below). What is the speed of the mass when it is at its lowest point? Express your answer in terms of m, L, and g. v = The position of a mass-on-a-spring oscillator is given by y = A sin(20t), where the value of t is in seconds and A = 0.44 m. What...
THE SIMPLE PENDULUM Pre-Lab 1. State the objectives of this experiment. 2. How do you measure...
THE SIMPLE PENDULUM Pre-Lab 1. State the objectives of this experiment. 2. How do you measure the length of a simple pendulum? 3. Define period of a simple pendulum in words. 4. The period of a simple pendulum is related to its length and the acceleration of gravity in an equation. Write down that equation. 5. What is the amplitude of a simple pendulum? 6. What does the period of a simple pendulum depend on? 7. True or false The...
A simple pendulum is created using a length (L) of string and a mass (M) attached...
A simple pendulum is created using a length (L) of string and a mass (M) attached to the end. Which of the following statements is true? a. As the acceleration due to gravity at a point increases the period of the pendulum decreases b. As the mass increases the period of the pendulum decreases c. As the acceleration due to gravity at a point increases the period of the pendulum increases d. As the length increases the period of the...
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...
w 3. Double-pendulum system (point mass) (see Textbook Example 2.5 if needed) Write the equations of...
w 3. Double-pendulum system (point mass) (see Textbook Example 2.5 if needed) Write the equations of motion (EOMs) for the No friction No friction double-pendulum system shown in Fig. 2. (c) Figure 1. Mass-Spring-Damper Systems Assume that the displacements of the pendulums are small enough to ensure that the spring is always horizontal (but DO NOT make small angle approximations when writing the EOMS). The pendulum rods are taken to be massless, of length L, and the springs are attached...
8. A simple pendulum is a point mass on a massless string, and T, = 2「/, A physical pendulum formed by a small mass on a lightweight string is approzimately a simple pendulum, but not quite, its period is T, 2n shorter than the period of a simple pendulum with the same length? Assume L is measured to the center of mass, and justify your answer. 2Vm L. Is the period of a physical pendulum longer or
Prob. 7.3: A simple pendulum (mass M and length L) is suspended from a cart (mass m) that canoscillate on the end of a spring of spring constant k, as shown in the figure at right. (a) Write the Lagrangian in terms of the generalized coordinates x and ?, where x is the extension of the spring from its equilibrium length and ? is the angle of the pendulum from the vertical. Find the two Lagrange equations. (b) Simplify the...
A simple pendulum has a rod of length LL with a bob of mass
m=0.100 kg at the end of the rod. The rod is supposed to be very
light and all the mass is imagined to be concentrated in the
bob.
A) What is the tension in the string when the pendulum swings by
an angle θ=5.00∘?
B) What is the magnitude of the restoring force on the bob when
θ=5.00∘?
C) If you drop a perpendicular from the...
A simple pendulum has a length L and a mass m. At its highest point, the pendulum mass is 0.25L above its lowest point (see figure below). What is the speed of the mass when it is at its lowest point? Express your answer in terms of m, L, and g. v = The position of a mass-on-a-spring oscillator is given by y = A sin(20t), where the value of t is in seconds and A = 0.44 m. What...
THE SIMPLE PENDULUM Pre-Lab 1. State the objectives of this experiment. 2. How do you measure the length of a simple pendulum? 3. Define period of a simple pendulum in words. 4. The period of a simple pendulum is related to its length and the acceleration of gravity in an equation. Write down that equation. 5. What is the amplitude of a simple pendulum? 6. What does the period of a simple pendulum depend on? 7. True or false The...
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...
w 3. Double-pendulum system (point mass) (see Textbook Example 2.5 if needed) Write the equations of motion (EOMs) for the No friction No friction double-pendulum system shown in Fig. 2. (c) Figure 1. Mass-Spring-Damper Systems Assume that the displacements of the pendulums are small enough to ensure that the spring is always horizontal (but DO NOT make small angle approximations when writing the EOMS). The pendulum rods are taken to be massless, of length L, and the springs are attached...
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