2. Vibrating Spring without Damping. A vibrating spring without damping can be modeled by the initial value problem (11) in Example 3 by taking b = 0. (a) If m= 10 kg, k = 250 kg/sec², y(0) = 0.3 m, and y' (0) = -0.1 m/sec, find the equation of motion for this undamped vibrating spring. (b) After how many seconds will the mass in part (a) first cross the equilibrium point? (c) When the equation of motion is of the form displayed in (9), the motion is said to be oscillatory with fre- quency B/27. Find the frequency of oscillation for the spring system of part (a).
2. Vibrating Spring without Damping. A vibrating spring without damping can be modeled by the initial value problem (11) in Example 3 by taking b = 0. (a) If m= 10 kg, k = 250 kg/sec², y(0) = 0.3 m, and y' (0) = -0.1 m/sec, find the equation of motion for this undamped vibrating spring. (b) After how many seconds will the mass in part (a) first cross the equilibrium point? (c) When the equation of motion is of the form displayed in (9), the motion is said to be oscillatory with fre- quency B/27. Find the frequency of oscillation for the spring system of part (a).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Linear Second Order equations
![**32. Vibrating Spring without Damping.**
A vibrating spring without damping can be modeled by the initial value problem (11) in Example 3 by taking \( b = 0 \).
(a) If \( m = 10 \, \text{kg}, \, k = 250 \, \text{kg/sec}^2, \, y(0) = 0.3 \, \text{m}, \) and \( y'(0) = -0.1 \, \text{m/sec} \), find the equation of motion for this undamped vibrating spring.
(b) After how many seconds will the mass in part (a) first cross the equilibrium point?
(c) When the equation of motion is of the form displayed in (9), the motion is said to be oscillatory with frequency \( \beta/2\pi \). Find the frequency of oscillation for the spring system of part (a).
**33. Vibrating Spring with Damping.**
Using the model for a vibrating spring with damping discussed in Example 3:
(a) Find the equation of motion for the vibrating spring with damping if \( m = 10 \, \text{kg}, \, b = 60 \, \text{kg/sec}, \, k = 250 \, \text{kg/sec}^2, \, y(0) = 0.3 \, \text{m}, \) and \( y'(0) = -0.1 \, \text{m/sec} \).
(b) After how many seconds will the mass in part (a) first cross the equilibrium point?
(c) Find the frequency of oscillation for the spring system of part (a). [*Hint: See the definition of frequency given in Problem 32(c).]
(d) Compare the results of Problems 32 and 33 and determine what effect the damping has on the frequency of oscillation. What other effects does it have on the solution?
**34. RLC Series Circuit.**
In the study of an electrical circuit consisting of a resistor, capacitor, inductor, and an...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e2a25b6-6671-4e82-b823-68b6d346fe5d%2F64f8e240-f8f6-4cad-92a0-d1915d904f9f%2F3ahe484_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**32. Vibrating Spring without Damping.**
A vibrating spring without damping can be modeled by the initial value problem (11) in Example 3 by taking \( b = 0 \).
(a) If \( m = 10 \, \text{kg}, \, k = 250 \, \text{kg/sec}^2, \, y(0) = 0.3 \, \text{m}, \) and \( y'(0) = -0.1 \, \text{m/sec} \), find the equation of motion for this undamped vibrating spring.
(b) After how many seconds will the mass in part (a) first cross the equilibrium point?
(c) When the equation of motion is of the form displayed in (9), the motion is said to be oscillatory with frequency \( \beta/2\pi \). Find the frequency of oscillation for the spring system of part (a).
**33. Vibrating Spring with Damping.**
Using the model for a vibrating spring with damping discussed in Example 3:
(a) Find the equation of motion for the vibrating spring with damping if \( m = 10 \, \text{kg}, \, b = 60 \, \text{kg/sec}, \, k = 250 \, \text{kg/sec}^2, \, y(0) = 0.3 \, \text{m}, \) and \( y'(0) = -0.1 \, \text{m/sec} \).
(b) After how many seconds will the mass in part (a) first cross the equilibrium point?
(c) Find the frequency of oscillation for the spring system of part (a). [*Hint: See the definition of frequency given in Problem 32(c).]
(d) Compare the results of Problems 32 and 33 and determine what effect the damping has on the frequency of oscillation. What other effects does it have on the solution?
**34. RLC Series Circuit.**
In the study of an electrical circuit consisting of a resistor, capacitor, inductor, and an...
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