The device pictured in the figure entertains infants while keeping them from wan

Question

The device pictured in the figure entertains infants while keeping them from wandering. The child bounces in a harness, with a spring constant k, and is suspended off of the ground. If the spring stretches X1 = 0.24 m from equilibrium while supporting an 8.05- kg child, what is its spring constant, in newtons per meter? Numeric : A numeric value is expected and not an expression. k = What is the time, in seconds, for one complete bounce of this child about the point X1 Numeric : A numeric value is expected and not an expression T= What is the child's maximum velocity, in meters per second, if the amplitude of her bounce, relative to xh is 0.21 m? Numeric : A numeric value is expected and not an expression

Explanation / Answer

here,

a)

x1= 0.24 m

mass of child , m = 8.05 kg

let the spring constant be k

m*g = k * x1

8.05 * 9.8 = k * 0.24

k = 328.71 N/m

the spring constant is 328.71 N/m

b)

time priod for one coplete bounce , T = 2 * pi* sqrt( m/k)

T = 2*pi*sqrt( 8.05/328.71)

T = 0.98 s

the timeperiod is 0.98 s

c)

amplitude , A = 0.21 m

child maximum velocity , vmax = A*w

vmax = A * 2*pi/T

vmax = 0.21 * 2*pi/0.98

vmax = 1.35 m/s

the maximum velocity is 1.35 m/s

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