? asked in Science & MathematicsPhysics · 1 decade ago

At t = 0, a 790 g mass at rest on the end of a horizontal spring (k = 130 N/m)?

At t = 0, a 790 g mass at rest on the end of a horizontal spring (k = 130 N/m) is struck by a hammer, which gives the mass an initial speed of 2.71 m/s.

(a) Determine the period of the motion.

.49 s

Determine the frequency of the motion.

2.04 Hz

(b) Determine the amplitude.

___ m

(c) Determine the maximum acceleration.

___ m/s2

(d) Determine the position as a function of time.

( ___ m ) sin[ ( ___ rad/s)t ]

(e) Determine the total energy.

___ J

I was able to figure out the first two parts but couldn't with the rest, any help would be appreciated

1 Answer

Relevance
  • O-360
    Lv 6
    1 decade ago
    Favorite Answer

    (a)

    ω = sqrt(k/m) = sqrt(130/.79) = 12.83 rad/sec

    f = ω/(2*π) = 2.04 Hz

    T = 1/f = 0.49 s

    (b)

    f = 2.04 Hz

    (c)

    The maximum acceleration occurs at the extremes of the oscillation, i.e. when the mass has come to rest. The initial velocity, at the uncompressed length, represents Kinetic Energy (KE):

    KE = (1/2)*m*v^2 = (1/2)*.79*(2.71)^2 = 2.9 J

    This equals the Potential Energy (PE) at maximum spring compression:

    PE = (1/2)*k*x^2 = KE = 2.9 J

    x^2 = 2*KE/k

    x = sqrt(2*KE/k) = sqrt( 2*2.9/130 ) = 0.211 m

    The force at this displacement is:

    F = k*x = 130*.211 = 27.5N

    F = m*a

    a = F/m = 27.5/.79 = 34.8 m/s^2

    (d)

    We determined the amplitude above, and we have the radian frequency from (a):

    x(t) = ( .211 m ) sin[ ( 12.83 rad/s)t ]

    (e)

    The total energy is equal to the initial KE, as derived in (c)

    E = 2.9 J

    • Login to reply the answers
Still have questions? Get your answers by asking now.