A thin uniform rod of length 3.00 m3.00 m executes simple harmonic oscillations like a physical pendulum with minimum time period. If the effective length of pendulum is x−−√ m𝑥 m. Find the value of x𝑥.
Question
A thin uniform rod of length 3.00 m3.00 m executes simple harmonic oscillations like a physical pendulum with minimum time period. If the effective length of pendulum is x−−√ m𝑥 m. Find the value of x𝑥.
Solution
The time period of a simple pendulum is given by the formula:
T = 2π √(L/g)
where: T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.
For a physical pendulum like a rod, the effective length L is the distance from the pivot point to the center of mass. For a uniform rod, the center of mass is at the midpoint, so the effective length is L/2.
The minimum time period occurs when the rod oscillates about an axis through its end, so the effective length is the full length of the rod, L.
Given that the rod is 3.00 m long, the effective length L is 3.00 m.
The question asks for the value of √L, so we take the square root of L:
√L = √3.00 m = 1.732 m
So, the value of x is 1.732.
Similar Questions
A pendulum is made by attaching a 4.00 kg mass to the end of a thin, massless rod. The period of small-amplitude oscillations of the pendulum is 1.00 sec. What is the length of the rod?
A grandfather clock uses a physical pendulum to keep time. The pendulum consists of a uniform thin rod of mass M = 1.61 kg and length L = 0.153 m that is pivoted freely about one end, with a solid disk of mass 3M and a radius of L4𝐿4 attached to the free end of the rod. Determine the length L that gives a period of T = 2.45 s.
A rod of length l,𝑙, mass m are connected to two springs of spring constant K𝐾 each. Find the frequency of small oscillation
A grandfather clock uses a physical pendulum to keep time. The pendulum consists of a uniform thin rod of mass M = 1.61 kg and length L = 0.153 m that is pivoted freely about one end, with a solid disk of mass 3M and a radius of L4𝐿4 attached to the free end of the rod. What the moment of inertia of the pendulum about its pivot point?
A pendulum is swinging with a period of 0.280 s.What is the frequency of the pendulum?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.