P16_024.PDF

2 kx acting in a direction so

as to return the block to its equilibrium position ( x = 0). Since the acceleration a = d 2 x/dt 2 ,Newton’s

second law yields

−

m d 2 x

dt 2 =

−

2 kx .

Substituting x = x m cos( ωt + φ ) and simplifying, we ﬁnd

ω 2 = 2 k

where ω is in radians per unit time. Since there are 2 π radians in a cycle, and frequency f measures

cycles per second, we obtain

2 k

m .

f = ω

2 π

24. When displaced from equilibrium, the net force exerted by the springs is

2 π =