math

posted by .

a steel ball weighing 128 lb is suspended from a spring, whereupon the spring is stretched 2 ft from its natural length. the ball is started in motion with no initial velocity by displacing it 6 in above the equilibrium position. assuming no damping force, find an expression for
a)the position of the ball at any time.
b)the position of the bal at t=pai/12 sec
c)the circular frequency, natural frequency and period for this system

  • math -

    k = 64 lb/ft for spring

    position above equilirium = x
    at t = 0 x = .5 ft
    so
    x = .5 cos 2 pi t/T
    we need to find T, the period
    f = -kx = m a
    but a = .5 (2 pi/T)^2(-cos2 pi/T) =-(2pi/T)^2 x
    so
    -k x = -(2 pi/T)^2 x
    2 pi/T = sqrt(k/m)
    m = 128/32 = 4
    so
    2 pi/T = sqrt (64/4) = 4
    therefore
    x = .5 cos 4 t

    at t = pi/12
    x = .5 cos pi/3 = .5 cos 60deg = .25

    w = 2 pi f = 2 pi/T = 4 radians/sec
    f = w/2pi = 2/pi
    T = pi/2

  • actually ancient physics -

    The question is really a physics question but uses old English units of feet which means to get mass (in slugs) you must divide pounds by g which is about 32 ft/s^2.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    A spring with a spring constant of 223.9 N/m is compressed by 0.220 m. Then a steel ball bearing of mass 0.0372 kg is put against the end of the spring, and the spring is released. What is the speed of the ball bearing right after …
  2. Physics - Eqilibrium position of a spring-ball

    A 275g ball is resting on top of the spring that is mounted on the floor. You exert a force of 325N on the ball and it compresses the spring 44.5cm. If you release the ball from the position, how high above the equilibrium position …
  3. physics

    A ball of mass 540 g hangs from a spring whose stiffness is 155 newtons per meter. A string is attached to the ball and you are pulling the string to the right, so that the ball hangs motionless, as shown in the figure. In this situation …
  4. physics

    The spring in the muzzle of a child's spring gun has a spring constant of 780 N/m. To shoot a ball from the gun, first the spring is compressed and then the ball is placed on it. The gun's trigger then releases the spring, which pushes …
  5. computer network engineering

    a steel ball weighing 128 lb is suspended from a spring, whereupon the spring is stretched 2 ft from its natural length. the ball is started in motion with no initial velocity by displacing it 6 in above the equilibrium position. assuming …
  6. College Physics

    A ball of mass 620 g hangs from a spring whose stiffness is 195 newtons per meter. A string is attached to the ball and you are pulling the string to the right, so that the ball hangs motionless, as shown in the figure. In this situation …
  7. Physics - Spring Gun

    A toy gun uses a spring to shoot a ball with a mass of 5.0 g. The spring is “loaded” by compressing it 5.0 cm and has a spring constant of 288 N/m. The end of the spring is at the end of the gun (the ball does not travel any distance …
  8. Physics!

    A spring with a spring constant of 224.3 N/m is compressed by 0.253 m. Then a steel ball bearing of mass 0.0433 kg is put against the end of the spring, and the spring is released. What is the speed of the ball bearing right after …
  9. Physics

    Using the definition of work, get a job on the tension of the spring with a spring constant 300,0 H / m 20,0sm. The spring stiffness of the spring gun with 400 Nm pro- ryadili bullet clenched spring by 5.0 cm. Weight 10.0 g bullet …
  10. physics

    a 2.2 kg ball is dropped from 3m above vertical spring whose spring constant is 450 n/m. a) how far will it compress the spring?

More Similar Questions