Question: A 1 kg block on a spring is modeled by the following initial value problem. x+4x= 12 cos(4t), x(0) = 0, x'(0) = 0

A 1 kg block on a spring is modeled by the following initial value problem. x"+4x= 12 cos(4t), x(0) = 0, x'(0) = 0 a) Find the position of the block at time t x(t) = b) Assuming the forcing function and the spring stay the same, what mass would the block have to have for the system to be in resonance? kg. (exact answer)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a To find the position of the block at time t we first need to solve the differential equation using ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Shaw Company has total stockholders' equity of $5,400,000. The company's outstanding capital stock includes 60,000 shares of $10 par value common stock and 15,000 shares of 6%, $50 par value...

Find the period and velocity for the following frequencies if the wavelength is 0.50 m: a) 0.30 Hz b) 400 s c) 30 cycles/s d) 5.0 kHz e) 102.1 MHz.

You have found the following stock quote for RJW Enterprises, Incorporated, in the financial pages of today's newspaper. YTD %Change -1.1 Stock RJW Enterprises SYM YLD PE Last Net Change RWJ 2.5 15...

Problem #1: In a murder investigation, the temperature of the corpse was 33 C at 1:30pm and 24 C 2 hours later. Normal body temperature is 37 C and the surrounding temperature was 8 C. How long (in...

Symbolic answers must be entered using notation similar to the examples given below. If you enter decimal numbers for questions that indicate that a symbolic answer is required, it will be marked as...

1. Suppose that the mass in a mass-springdashpot system with m = 10, c = 7 and k = 1 is set in motion with x(0) = O and x'(0) = 4. (3) Find the position function x(t) and show x that its graph looks...

7 L 'LJ' :! OR? T * [4 ! 715 n rip ti up qi x r' '=(91nmnvmic :I;J = D Spring 2017 Stony Brook University Snliyaisachi Muklusrjeo, Matthew Dnnnonlmrg Problem Set 6 Differential Equations with Linear...

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Ronald Roth started his new job as controller with Aerosystems today. Carole, the employee benefits clerk, gave Ronald a packet that contains Information on the company's health insurance options....

Calculus 3 Section 13.2 Reading Assignment: Integrals of Vector Functions Question 2. Read the introduction to the subsection "The Vector and Parametric Equations for Ideal Projectile Motion" (p. 774...

Determine the constants c and n in Equation 12-2 that describe the rate of crystallization of polypropylene at 140 C. (See Figure 12-30.)

AVP Company processes an average of 400 vouchers payable every month. Each voucher package contains a copy of the check disbursed and supporting and supporting documents such as vendor invoices,...

Case Management and the Service Delivery Process Consider this statement written by Stephen Moore (1992): "case management has been conceptualized as a mechanism for coordinating services in a...

Contrast the main differences between the Models 7113 and 7152 in the 6. Avery-Denison Range of Universal Testing Machines.

2. Mass 1 is moving according to the law x-3t'. Assuming corresponding values for radia of corresponding discs, determin in a general way total accelaration in a point M 4.

2. Mass 1 is moving according to the law x=3t. Assuming corresponding values for radia of corresponding discs, determine in a general way total accelaration in a point M 7. -3

Mass 1 is moving according to the law x=3t^3. Assuming corresponding values for radia of corresponding discs, determine in a general way total acceleration in a point M M. 3 1. 15

6 Theory of Machines 5. A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and...

The system in Problem 19, like the system in (2), canbe solved with no advanced knowledge. Solve for x(t) and y(t) and compare their graphs with your sketches in Problem 19. Determine the limiting...

Consider two tanks A and B, with liquid being pumped in and out at the same rates, as described by the system of equations (3). What is the system of differential equations if,instead of pure water,...

What is the concentration c(t) of the salt in the tank at time t? At t = 5 min? What is the concentration of the salt in the tank after a long time, that is, as t ? At what time is the concentration...

Which schools of management thought are illustrated in this case?

Prepare a basic outline of complexity theory and explain its relevance to business.

Discuss why knowledge of the evolution of management theories is important to managers