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(a) Consider a pendulum with a mass m suspended at the end of a light string...
A pendulum consists of a mass m suspended from a string of length L. When the...
A pendulum consists of a mass m suspended from a string of length L. When the pendulum is swinging, how much greater is the mass’s potential energy when the string is displaced from the vertical by the angle θ than when the mass is at the lowest position?
A simple pendulum (mass M and length L) is suspended from a cart of mass m...
A simple pendulum (mass M and length L) is suspended from a cart of mass m that moves freely along a horizontal track shown at right. You might find it helpful to introduce the dimensionless parameters η-m/M and wo- /g/L. a What are the normal frequencies of small oscillations of the system (0 <1)? b Find and describe the corresponding normal modes of the system. c The cart/pendulum systern is held at rest in the configuration x-0 and θ K...
22*. A point mass on the end of a light string rotates as a conical pendulum...
22*. A point mass on the end of a light string rotates as a conical pendulum with angular velocity ω, the string being inclined at an angle θ to the vertical. Show that if the motion is slightly disturbed the result- ing small oscillations have an angular frequency o(1 +3 cos20)+.
Consider a conical pendulum with a bob of mass m = 75.0 kg on a string...
Consider a conical pendulum with a bob of mass m = 75.0 kg on a string of length L = 10.0 m that makes an angle of 0 = 7.00° with the vertical. (Consider +î to be towards the center of the circular path and +ġ to be upward.) m (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum.
Conical Pendulum A mass attached at the end of a massless string swings around in a...
Conical Pendulum A mass attached at the end of a massless string swings around in a horizontal circle (the string sweeps out a cone). Let θ be the angle the string makes with the vertical, l be the length of the string, h is the vertical height of the string, and r is the radius of the circle. So, l is the hypotenuse of a right triangle with h and r as legs, and θ as the upper angle. The...
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...
Conservation of Energy A simple pendulum consists of an object suspended by a string. The object...
Conservation of Energy A simple pendulum consists of an object suspended by a string. The object is assumed to be a particle. The string, with its top end fixed, has negligible mass and does not stretch. In the absence of air friction, the system oscillates by swinging back and forth in a vertical plane. If the string is 1.50 m long and makes an initial angle of 34.5° with the vertical, calculate the speed of the particle at the following...
1. (20 points) A pendulum consists of a small ball of mass m=2.00 kg that is...
1. (20 points) A pendulum consists of a small ball of mass m=2.00 kg that is suspended from a fixed point by a light string of length L=0.850 m (like the demonstration video.) The pendulum is released from rest when it is in its initial position with 0 =65.0°. Air resistance is negligible. a) Calculate the work done by gravity as the ball moves from the highest point of its semicircular path to the lowest point of its path. b)...
Consider a damped pendulum consisting of a ball of mass M and radius a suspended by...
Consider a damped pendulum consisting of a ball of mass M and radius a suspended by a fine wire of length L below a pivot. The ball is moving through a fluid of viscosity y, and this retards its motion. It is assumed that the ball moves sufficiently slowly that Stokes law applies. Under these conditions, the equation describing the motion of the sphere is given by ML =-Mg sin 0 - 6xual, The initial conditions are 012-= 0, and...
A Pendulum with air resistance Pendula are widely used in applications including accelerometers and seismometers and...
A
Pendulum with air resistance Pendula are widely used in applications including accelerometers and seismometers and are a model system to study vibrations and damping. Consider a pendulum comprising a small mass m that is connected by a thin massless rod of length l to a hinged support The hinge is frictionless but the mass experiences air resistance as it swings. The air drag force on the mass is Fdrag-kv |v, where v is the velocity of the mass and...
A simple pendulum (mass M and length L) is suspended from a cart of mass m that moves freely along a horizontal track shown at right. You might find it helpful to introduce the dimensionless parameters η-m/M and wo- /g/L. a What are the normal frequencies of small oscillations of the system (0 <1)? b Find and describe the corresponding normal modes of the system. c The cart/pendulum systern is held at rest in the configuration x-0 and θ K...
22*. A point mass on the end of a light string rotates as a conical pendulum with angular velocity ω, the string being inclined at an angle θ to the vertical. Show that if the motion is slightly disturbed the result- ing small oscillations have an angular frequency o(1 +3 cos20)+.
Consider a conical pendulum with a bob of mass m = 75.0 kg on a string of length L = 10.0 m that makes an angle of 0 = 7.00° with the vertical. (Consider +î to be towards the center of the circular path and +ġ to be upward.) m (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum.
1. (20 points) A pendulum consists of a small ball of mass m=2.00 kg that is suspended from a fixed point by a light string of length L=0.850 m (like the demonstration video.) The pendulum is released from rest when it is in its initial position with 0 =65.0°. Air resistance is negligible. a) Calculate the work done by gravity as the ball moves from the highest point of its semicircular path to the lowest point of its path. b)...
Consider a damped pendulum consisting of a ball of mass M and radius a suspended by a fine wire of length L below a pivot. The ball is moving through a fluid of viscosity y, and this retards its motion. It is assumed that the ball moves sufficiently slowly that Stokes law applies. Under these conditions, the equation describing the motion of the sphere is given by ML =-Mg sin 0 - 6xual, The initial conditions are 012-= 0, and...
A
Pendulum with air resistance Pendula are widely used in applications including accelerometers and seismometers and are a model system to study vibrations and damping. Consider a pendulum comprising a small mass m that is connected by a thin massless rod of length l to a hinged support The hinge is frictionless but the mass experiences air resistance as it swings. The air drag force on the mass is Fdrag-kv |v, where v is the velocity of the mass and...
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