Simple harmonic motion and damped oscillations

Simple harmonic motion and damped oscillations Quiz

Spec 9.7–8 · Edexcel A-Level Further Maths: Quiz

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  1. 1. A particle satisfies x¨=−9x\ddot{x}=-9x. What is its period?

    • A. π3\frac{\pi}{3}
    • B. 6π6\pi
    • C. 2π3\frac{2\pi}{3}
    • D. 23π\frac{2}{3\pi}

  2. 2. A particle has x=3cos⁡2tx=3\cos2t. What is its maximum speed?

    • A. 6
    • B. 12
    • C. 3
    • D. 1.5

  3. 3. What type of damping is x¨+8x˙+16x=0\ddot{x}+8\dot{x}+16x=0?

    • A. Light
    • B. Heavy
    • C. None
    • D. Critical

  4. 4. x=e−2tcos⁡3tx=e^{-2t}\cos3t. By what factor does the displacement multiply in each period of the oscillation?

    • A. e−2e^{-2}
    • B. e−4π/3e^{-4\pi/3}
    • C. e−3e^{-3}
    • D. e−2πe^{-2\pi}

  5. 5. In the forced vibration x¨+2x˙+5x=10cos⁡t\ddot{x}+2\dot{x}+5x=10\cos t, what governs the long-term motion?

    • A. The complementary function
    • B. The initial conditions
    • C. The particular integral
    • D. The mass only

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