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the position of a 0.5 kg obj The position of a 0.5 kg object connected to a spri

ID: 2077411 • Letter: T

Question

the position of a 0.5 kg obj The position of a 0.5 kg object connected to a spring varies with time according to the expression x = (24 cm) sin (0.2 pi t). a) Find the period of this motion. b) Find the frequency of this motion. c) Find the spring constant. d) Find the amplitude of the motion. e) Find the total energy of the motion. f) Find the maximum speed of the motion. g) At what time is the maximum speed attained? h) Find the first time after t = 0 that the object reaches the position x = 16.

Explanation / Answer

here,

mass , m = 0.5 kg

x = 24 cm * sin(0.2 * pi * t)

angular frequency , w = 0.2 * pi

a)

the period of this motion , T = 2 * pi /w

T = 2 * pi /( 0.2 * pi)

T = 10 s

b)

the frequency of motion , f = 1/T

f = 0.1 Hz

c)

let the spring constant be k

sqrt(k/m) = w

sqrt(k/0.5) = 0.2 * pi

k = 0.197 N/m

d)

the amplitude of motion is 24 cm