Classical Mechanics

Simple Harmonic Motion

Periodic Motion

         

A body of mass m=4 kg m = 4 \text{ kg} is attached to a spring that hangs from the ceiling. If the spring is held at its original length and then let go, the body oscillates with amplitude A=ab m, A = {\frac{a}{b}} \text{ m}, where aa and bb are coprime positive integers. Find the value of a+b.a+b.

The spring constant is k=5 N/m k = 5 \text{ N/m} and the gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

A ring of mass M=5 kg M = 5 \text{ kg} and radius R=3 m R = 3 \text{ m} oscillates on a horizontally placed rod. If the ring's angular frequency can be expressed as ω=ab rad/s, \omega = \sqrt{\frac{a}{b}} \text{ rad/s}, where aa and bb are coprime positive integers, what is the value of a+b?a+b?

The moment of inertia is given by I=2MR2 I = 2MR^2 and the gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

A body of mass m=8 kg m = 8 \text{ kg} oscillates on a spring hanging from the ceiling with an angular frequency of ω=ab rad/s, \omega = \sqrt{\frac{a}{b}} \text{ rad/s}, where aa and bb are coprime positive integers. Find the value of a+b.a+b.

The spring constant is k=5 N/m k = 5 \text{ N/m} and the gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

In the figure above, a body of mass m=4 kg m = 4 \text{ kg} oscillates in the middle of two identical springs with an angular speed of ω=ab rad/s, \omega = \sqrt{\frac{a}{b}} \text{ rad/s}, where aa and bb are coprime positive integers. Find the value of a+b.a+b.

The spring constant is k=9 N/m k = 9 \text{ N/m} and the gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

A pendulum of mass m=5 kg m = 5 \text{ kg} and length L=12 m L = 12 \text{ m} oscillates with an angular frequency of ω=ab rad/s, \omega = \sqrt{\frac{a}{b}} \text{ rad/s}, where aa and bb are coprime positive integers. Find the value of a+b.a+b.

The gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

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