Pendulum Motion and Small Angle Approximation

The video tutorial explains the physics of a pendulum, focusing on the forces acting on it, such as gravity and tension. It discusses decomposing these forces into x and y components and introduces differential equations to describe the pendulum's motion. The tutorial then explores the small angle approximation, which simplifies the equations, leading to a solution that describes simple harmonic motion. The period of the pendulum is derived, and the limitations of the small angle approximation are highlighted.

What are the two forces acting on the pendulum?

• Gravity and tension

• Tension and magnetic force

• Gravity and friction

• Tension and air resistance

How is the tension decomposed in the pendulum system?

• Into gravitational and magnetic components

• Into horizontal and vertical components

• Into kinetic and potential components

• Into x and y components

What is the restoring force in the x direction for the pendulum?

• Gravity times sine of theta

• Gravity times cosine of theta

• Tension times sine of theta

• Tension times cosine of theta

What is the small angle approximation used for in pendulum motion?

• To assume the angle is always zero

• To approximate the pendulum's period

• To simplify the equations of motion

• To simplify the calculation of tension

What happens to the cosine of theta under the small angle approximation?

• It becomes equal to theta

• It becomes zero

• It becomes negative

• It becomes very close to one

Why is the acceleration in the y direction considered negligible under the small angle approximation?

• Because the y excursion is much smaller than the x excursion

• Because the pendulum does not move in the y direction

• Because gravity cancels out the y acceleration

• Because the tension is too strong

What type of motion does the pendulum exhibit under the small angle approximation?

• Linear motion

• Random motion

• Circular motion

• Simple harmonic motion

What is the formula for the period of a pendulum under the small angle approximation?

• 2π times the square root of g over l

• 2π times the square root of l over g

• 2π times the square root of m over k

• 2π times the square root of k over m

What is a key restriction of the pendulum model discussed?

• The mass must be concentrated at a point

• The string must be elastic

• The pendulum must be in a vacuum

• The angle must be large

What is assumed about the string in the pendulum model?

• It is flexible

• It is rigid

• It is elastic

• It is massless