Lesson 4.10f-g
4.10f-g Simple harmonic motion and damped oscillations Quiz: OCR Further Maths, Unit 1
20 questions
In partnership with Revision Ninja
Lesson 4.10f-g, Simple harmonic motion and damped oscillations: 20 multiple choice questions for the OCR Further Maths (H245), Unit 1: Pure Core (Y540, Y541), written with Revision Ninja.
Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.
The 20 questions
-
What second-order differential equation defines simple harmonic motion with parameter ω?
- d²x/dt² = -ωx
- d²x/dt² = ω²x
- d²x/dt² = -ω²x
- dx/dt = -ω²x
-
What is the period T of a system undergoing simple harmonic motion with parameter ω?
- 2πω
- π/ω
- 2π/ω
- ω/2π
-
What type of damping occurs when the auxiliary equation has two distinct real roots?
- Overdamping
- Underdamping
- Critical damping
- No damping
-
What condition on discriminant b² - 4ac gives light damping in a damped oscillator?
- b² - 4ac ≥ 0
- b² - 4ac > 0
- b² - 4ac < 0
- b² - 4ac = 0
-
Which damping regime allows a system to return to equilibrium in the shortest time without oscillating?
- Critical damping
- Underdamping
- Overdamping
- Heavy damping
-
What is the expression for maximum speed in simple harmonic motion with amplitude A?
- ωA
- 0.5ωA
- ωA²
- ω²A
-
What is the expression for maximum acceleration magnitude in simple harmonic motion with amplitude A?
- ω²A
- ωA²
- ωA
- 2ω²A
-
What is the period of SHM represented by the differential equation d²x/dt² + 16x = 0?
- 4π
- π/4
- π/2
- 2π
-
If d²x/dt² = -9x and maximum displacement is 3, what is the maximum speed?
- 3
- 81
- 27
- 9
-
A system has equation d²x/dt² + 6 dx/dt + 9x = 0. What damping type is this?
- Overdamping
- Forced damping
- Critical damping
- Underdamping
-
A system has equation d²x/dt² + 4 dx/dt + 13x = 0. What damping type is this?
- Critical damping
- Light damping
- Zero damping
- Heavy damping
-
What is the frequency in hertz of simple harmonic motion with equation d²x/dt² + 100π²x = 0?
- 100
- 10
- 50
- 5
-
In SHM with ω = 2 and amplitude 5, what is the speed when displacement x = 3?
- 8
- 10
- 4
- 6
-
For d²x/dt² + 5 dx/dt + 4x = 0, what is the general solution form?
- Ae^(-t) + Bte^(-4t)
- (A + Bt)e^(-2t)
- e^(-t)(A cos 4t + B sin 4t)
- Ae^(-t) + Be^(-4t)
-
What is the maximum acceleration of an object in SHM with x = 4 cos(3t)?
- 36
- 12
- 9
- 4
-
An oscillator d²x/dt² + k dx/dt + 25x = 0 is critically damped. What is positive k?
- 50
- 20
- 10
- 5
-
In SHM, maximum speed is 12 and maximum displacement is 4. What is parameter ω?
- 12
- 4
- 3
- 48
-
For what positive range of k does d²x/dt² + k dx/dt + 16x = 0 exhibit oscillations?
- k < 16
- k > 16
- k < 8
- k > 8
-
If x = e^(-2t) cos(3t) models damped motion, what is the pseudo-period of oscillation?
- 2π/3
- π/3
- 3π/2
- 2π/2
-
What equation relates speed v, displacement x, amplitude A, and parameter ω in SHM?
- v² = ω²(x² - A²)
- v² = ω²(A² - x²)
- v = ω(A - x)
- v² = ω²(A² + x²)
Related quizzes
- Proof by induction Quiz · 4.01 · 20 questions
- Complex numbers: language and arithmetic Quiz · 4.02a-d · 20 questions
- Modulus-argument form, polynomial roots and Argand diagrams Quiz · 4.02e-n · 20 questions
- Loci, de Moivre's theorem and roots of unity Quiz · 4.02o-s · 20 questions
- Matrix language, linear transformations, invariance and determinants Quiz · 4.03a-h · 20 questions
- Matrix inverses, simultaneous equations and planes meeting Quiz · 4.03n-t · 20 questions
- Vector equations of lines and planes, scalar product Quiz · 4.04a-c · 20 questions
- Vector product, intersections and shortest distances Quiz · 4.04e-h · 20 questions
- Relationships between roots and coefficients; partial fractions Quiz · 4.05a-c · 20 questions
- Summation of series and the method of differences Quiz · 4.06a-b · 20 questions