physics

A science museum has asked you to design a simple pendulum that will make 25.0 complete swings in 85.0 {\rm s}.

How long should the pendulum be? in meters

  1. 👍 0
  2. 👎 0
  3. 👁 1,138
  1. No book handy so will derive pendulum
    let theta be angle from vertical then
    (1/2) m v^2 max = m g h = m g L (1- (1-theta^2/2)) maximum

    (1/2) v^2 = g L(theta^2/2)
    but v = L d theta/dt

    L^2 d (theta/dt)^2 = g L theta^2
    let Theta = A sin 2 pi t/T
    max = A
    then d theta/dt = A (2 pi/T) cos 2pit/T
    max = A(2 pi /T)
    so
    L (2 pi/T)^2 = g
    2 pi/T = sqrt(g/L)
    T = 2 pi sqrt(L/g)

    so now the problem
    T =85/25 = 3.4 seconds per swing
    2 pi/T = 1.85
    T^2 = 3.42 = L/9.81
    L = 33.5 m

    1. 👍 0
    2. 👎 1
  2. T =85/25 = 3.4 seconds per swing
    T/2pi = .541 = sqrt(L/9.8)
    L/9.8 = .293
    L = 2.87 m

    1. 👍 2
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    The Length of time (T) in seconds it takes the pendulum of a clock to swint through one complete cycle is given by the formula T=2pie square root of 7 divided by 32 where L is the length in feet, of the pendulum, and pie is

  2. Math

    The length of time (T) in seconds it takes the pendulum of a clock to swing through one complete cycle is givenby the formula T=2pi square root of L divided by 32 where L is the length in feet, of the pendulum, and pi is

  3. math

    The formula T=2*pi*sqrt[L/g] gives the period of a pendulum of length l feet. The period P is the number of seconds it takes for the pendulum to swing back and forth once. Suppose we want a pendulum to complete three periods in 2

  4. Math-Pre Cal & Trig

    A pendulum swings uniformly back and forth, taking 2 seconds to move from the position directly above point A to the position directly above point B. . . . . _______________._______________ A . B . (SIMPLE DRAWING) The distance

  1. physics

    If the pendulum’s length is 2.00 m and ag =9.80 m/s , how many complete oscillations does the pendulum make in 5.00 min? the answer is 106 but how do i find it !!

  2. wcccd

    The period p of a pendulum, or the time it takes for the pendulum to make one complete swing, varies directly as the square root of the length L of the pendulum. If the period of a pendulum is 1.3 s when the length is 2 ft, find

  3. math

    The formula T=2*pi*sqrt[L/32] gives the period of a pendulum of length l feet. The period P is the number of seconds it takes for the pendulum to swing back and forth once. Suppose we want a pendulum to complete three periods in 2

  4. physics

    If you were asked to design a capacitor in which small size and large capacitance were required, what factors would be important in your design?

  1. Physics

    The oscillation of a single pendulum is 2.05s. What is the period of another simple pendulum which makes 300 vibration in the time it takes the first pendulum to make 200 vibrations?

  2. physics

    The length of a simple pendulum is 0.79m and the mass of the particle at the end of the cable is 0.24 kg. The pendulum is pulled away from its equilibrium position by an angle of 8.5 degrees and released from rest. Assume that

  3. maths

    A pendulum of length l metres takes t seconds to complete one full oscillation. The formula for T is: T = 2π √(l/g) Where g m/s2 is the acceleration due to gravity. a) Find T if l = 5 and g = 10 b) Rearrange the formula to make

  4. physics

    a simple pendulum with the length of 2.08m oscillates. the acceleration of gravity is 9.8 m/s^2.how many complete oscillations does the pendulum make in 3.75 min?

You can view more similar questions or ask a new question.