Simple Pendulum - Simple Harmonic Motion Derivation using Calculus

The video tutorial covers the derivation of simple harmonic motion equations for a simple pendulum using calculus. It begins with a review of the pendulum period equation and the definition of a simple pendulum, highlighting assumptions like negligible string mass and point mass bob. The tutorial then derives the restoring force and applies the small angle approximation to simplify equations. It concludes with the derivation of angular frequency and period, and a clarification on the dual meaning of omega in pendulum equations.

What is the equation for the period of a simple pendulum?

• 2 pi times the square root of the mass over spring constant

• 2 pi times the square root of the length over gravitational field strength

• 2 pi times the square root of the spring constant over mass

• 2 pi times the square root of the gravitational field strength over length

Which of the following is NOT an assumption made for a simple pendulum?

• The string is elastic

• The pendulum bob is a point mass

• The string has negligible mass

• There is no friction

What is the restoring force in a pendulum?

• The centripetal force

• The tension in the string

• The component of gravity acting tangentially

• The force of gravity acting vertically

Why is there a negative sign in the equation for tangential acceleration?

• Because the force is always parallel to the displacement

• Because the force is always directed towards equilibrium

• Because the force is always directed away from equilibrium

• Because the force is always perpendicular to the displacement

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

• To equate tangent of theta to theta for small angles

• To equate cosine of theta to theta for small angles

• To equate secant of theta to theta for small angles

• To equate sine of theta to theta for small angles

At what angle is the small angle approximation considered valid?

• Less than 15 degrees

• Less than 10 degrees

• Less than 5 degrees

• Less than 20 degrees

How is angular frequency for a simple pendulum calculated?

• Square root of spring constant over mass

• Square root of mass over spring constant

• Square root of pendulum length over gravitational field strength

• Square root of gravitational field strength over pendulum length

What is the relationship between period and angular frequency?

• Period equals angular frequency divided by 2 pi

• Period equals 2 pi divided by angular frequency

• Period equals angular frequency times 2 pi

• Period equals 2 pi times angular frequency

In the context of pendulum motion, what does omega represent?

• Only angular frequency

• Only angular velocity

• Both angular velocity and angular frequency

• Neither angular velocity nor angular frequency

What should be used in equations for a simple pendulum?

• Degrees

• Radians

• Gradians

• Turns