In the expression for the period of a simple pendulum, we do not take into account the mass that is hanging from the string. How is it possible that the mass does not affect the period of the pendulum? It was stated that the displacement that started the pendulum was small. What would happen if we started the pendulum with an extremely large displacement? The Hint given to me was: What happens when you attempt to swing higher and higher on a swing set?

Solution Preview

Hello and thank you for posting your question to Brainmass!
The solution is attached below in two files. the files are identical in content, only ...

... But we can figure out if these equations give the correct expression for angular velocity or period for known cases such as a simple pendulum and a vertically ...

... the expression derived before. 33. The simple pendulum in a grandfather clock is 1.0 m long. What are (a) the period and (b) the frequency of this pendulum? ...

... (b) Obtain an expression for the period of the pendulum for small oscillations. ... (b) Obtain an expression for the period of the pendulum for small oscillations. ...

... Radical expressions, equations and quadratic formulas are determined. ... The period T (time in seconds for one complete cycle) of a simple pendulum is related ...

... to the length L (in feet) of the pendulum by the ... Time Together and Alone, Length of Diagonal and Period of Swing ... Simplifying algebraic expressions is also shown ...

... contains 4 pages providing full step-by-step explanations and derivations of the required expressions and numerical ... The period of a simple pendulum is given ...

... Question #5: 10 points Rewrite the following quantity as an algebraic expression of x and state the domain on which ... 5. What is T1, the period of pendulum #1 ...

... b) Show that by differentiation your expression for E ... that the motion is periodic with period τ ... one-dimensional system is the simple pendulum, consisting of ...

... From the above mathematical expression, we can conclude that,. ... Either it should have been mentioned that the initial period of the pendulum was 1.000s and ...

... React to and imitate the facial expressions of others ? ... Language is an expression of symbolic function and ... that has developed over this period is reflective ...