Respuesta :
Answer:
v = 6.283 m/s
Explanation:
Given:
mass of the object, m = 1.00kg
The next time the speed is zero is at t = 0.200s i.e the one half of a total oscillation.
thus,
The time (T) for one complete oscillation will be = 2 × 0.200s = 0.4s
Now,
we know time period (T) is given as:
[tex]T=2\pi \sqrt\frac{m}{k}[/tex]
where, k is the spring constant
substituting the values in the above equation we get
[tex]0.4=2\pi \sqrt\frac{1}{k}[/tex]
or
[tex]\frac{m}{k} = (\frac{0.4}{2\pi})^2[/tex]
or
k = 246.70 N/m
Then, using the concept of conservation of energy, we have
[tex]\frac{1}{2}kx^2=\frac{1}{2}mv^2[/tex]
where,
x is the displacement in the spring
v = speed of the object
substituting the values in the above equation we get
[tex]\frac{1}{2}246.70\times 0.400^2=\frac{1}{2}1\times v^2[/tex]
or
[tex]19.73\times 2= v^2[/tex]
or
v = 6.283 m/s  (Answer)
