An object attached to a horizontal spring is oscillating back and forth along a frictionless surface. The maximum speed of the object is 1.91 m/s, and its maximum acceleration is 6.11 m/s2. How much time elapses betwen an instant when the object's speed is at a maximum and the next instant when its acceleration is at a maximum?
CAN ANYONE SOLVE THIS
CAN ANYONE SOLVE THIS
-
In simple harmonic motion(SHM) V(max) = A*w, here w is the angular frequency.
a(max) = A*w^2. Substituting numbers:
1.91 = A*w
6.11 = A*w^2
Dividing the above equation we have: (6.11) / (1.91) = (Aw^2) / (Aw) => w = 3.20. Since T = (2 pi)/w =>
T = 1.96 s. It takes a quarter of the period from the maximum speed (central position) to the maximum acceleration ( maximum displacement) therefore the time = T / 4 = 0.49 s
a(max) = A*w^2. Substituting numbers:
1.91 = A*w
6.11 = A*w^2
Dividing the above equation we have: (6.11) / (1.91) = (Aw^2) / (Aw) => w = 3.20. Since T = (2 pi)/w =>
T = 1.96 s. It takes a quarter of the period from the maximum speed (central position) to the maximum acceleration ( maximum displacement) therefore the time = T / 4 = 0.49 s