Answer to Question #96449 in Classical Mechanics for Surej

Question

Which has a greater velocity at the equilibrium position?
a. A 1kg mass attached to a spring of K=100N/m in horizontal frictionless
surface after releasing it from a compression of 10cm.
b. A 1kg mass oscillating on a concave-upward smooth surface with an
effective vertical height of 5cm.
c. A pendulum bob of mass 1kg displaced through a vertical height of 10cm.
d. All of these could not be compared.

Answer 1

a.

$$v=x\sqrt{\frac{k}{m}}=0.1\sqrt{\frac{100}{1}}=1\frac{m}{s}$$

b.

$$v=\sqrt{2gh}=\sqrt{2(9.8)(0.05)}=0.99\frac{m}{s}$$

c.

$$v=\sqrt{2gh}=\sqrt{2(9.8)(0.1)}=1.4\frac{m}{s}$$

Answer: c.