13. When two springs, suspended parallel to each other, are connected by a bar a

Question

13. When two springs, suspended parallel to each other, are connected by a bar at their bottom, they act as if they were one spring. The spring constant of the system is then equal to the sum of the spring constant of each spring. Assume a weight of 8 lb will stretch one spring 2 in. and the other spring 3 in. (a) What is the spring constant of each spring? (b) If the two springs are suspended p to each other and connected by a bar at their bottom, what is the spring constant of the system? (c) If a weight of 8 lb is attached to the system, brought to rest, and then released after being displaced 6 in., find the amplitude, period, and frequency of the motion.

Explanation / Answer

a)we know that

mg = kx => k = mg/x

K1 = 8 lb/0.17 ft = 47.06 lb/ft

K2 = 8 lb/0.25 = 32 lb/ft

Hence, K1 = 47.06 lb/ft ; K2 = 32 lb/ft

b)K = K1 + K2

K = 47.06 + 32 = 76.06 lb/ft

Hence, K = 76.06 lb/ft

c)x = 6 in

A = 6 in = 0.5 ft

w = sqrt (k/m) = sqrt (76.06/8) = 3.1 rad/s

f = w/2 pi = 3.1/2 x 3.14 = 0.49 Hz

T = 1/f = 1/0.49 = 2.04 s

Hence, A = 6 in ; w = 3.1 rad/s ; f = 0.49 Hz ; T = 2.04 s

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.