A difficult differential problem to solve.

  • Context: Undergrad 
  • Thread starter Thread starter imam07
  • Start date Start date
  • Tags Tags
    Differential
Click For Summary
SUMMARY

The discussion focuses on solving a challenging differential equation related to physics, specifically the motion of an object under gravity. The equation presented is y = y0 - (t + (e^-bt) - 1)(g/b^2), which simplifies to y = y0 - 1/2 gt^2. Participants are encouraged to find velocity and acceleration as functions of time and to approximate the function using its second-degree Maclaurin polynomial.

PREREQUISITES
  • Differential equations
  • Maclaurin series approximation
  • Basic physics of motion under gravity
  • Understanding of exponential functions
NEXT STEPS
  • Study differential equations in physics
  • Learn about Maclaurin series and their applications
  • Explore the principles of motion under gravity
  • Investigate the properties of exponential functions
USEFUL FOR

Students in physics, educators teaching differential equations, and anyone seeking to deepen their understanding of motion under gravity and mathematical approximations.

imam07
Messages
1
Reaction score
0
i have been assigned a series of Q from my physics class and i find this Q hard to solve. give me a clue how to approach. help would be better appreciated.

show for short time y= yo -(t+(e^-bt)-1)(g/b^2) reduces to * y=y0 -1/2 gt^2

* find velocity and acceleration as a function of time.
 
Physics news on Phys.org
Approximate the function by its second degree MacLaurin polynomial.
 

Similar threads

Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Solving Differential Equation Using Reduction of Order
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Can I Differentiate Both Sides to Solve y in y^2=ln(1-y^2)?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Partial Differential Equation solved using Products
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad General solution vs particular solution
  • · Replies 52 ·
2
Replies
52
Views
9K
Undergrad Determining equilibrium solutions to differential equations
  • · Replies 16 ·
Replies
16
Views
4K
Undergrad On vibrating string and differentiating infinite sum
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Verifying properties of Green's function
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Find the general solution for the differential equation
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Differential equation using power series method
  • · Replies 8 ·
Replies
8
Views
4K