At t = 0, a 800 g mass at rest on the end of a horizontal spring (k = 123 N/m) i

Question

At t = 0, a 800 g mass at rest on the end of a horizontal spring (k = 123 N/m) is struck by a hammer, which gives the mass an initial speed of 2.74 m/s.
At t = 0, a 800 g mass at rest on the end of a horizontal spring (k = 123 N/m) is struck by a hammer, which gives the mass an initial speed of 2.74 m/s.

(a) Determine the period of the motion.
__s
Determine the frequency of the motion.
__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.

Explanation / Answer

A)

Period of motion = 2pi* square root(m/k) = 2*pi*(.8/123) = 0.04

Frequency = 1/period = 1/0.04 = 25Hz

B)

Let amplitude = A
=> .5 kA^2 = .5mv^2
=> 123*A^2 = .8*2.74^2
=> A = square root(.8*2.74^2/123) = 0.22m

C)

maximum acceleration = A^2

and = 2pi*frequency = 157.07

max acc = 157.07^2*.22 =5427.6

D)

x= x_0 + Asin(t)

x(t) = 0.22sin(157.07*t)

E)

Total enery = .5mV^2 = .5*.8*2.74^2 =3J

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