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SHM systems: pendulums and springs questions
Two real oscillators carry the theory, a mass on a spring and a pendulum on a string. Each has a two-variable period formula, an energy see-saw between kinetic and potential, and a slow leak called damping.
19 original questions · 56 marks · the shm systems: pendulums and springs notes · Periodic motion
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State the equation for the period of a mass–spring system, defining each symbol.
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T = 2π√(m/k) (1), where T is the period, m the oscillating mass and k the spring constant (1).Calculate the period of a simple pendulum of length 1.0 m (g = 9.81 m s−2).
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T = 2π√(l/g) = 2π√(1.0/9.81) (1)
T = 2.01 s (1)State how the kinetic energy and potential energy of an oscillator vary during one oscillation.
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They interchange: kinetic energy is greatest at the equilibrium position (where potential energy is least) (1), and potential energy is greatest at the extremes (where kinetic energy is zero) (1). The total energy stays constant.State the condition under which the motion of a simple pendulum is simple harmonic.
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The oscillations must be of small amplitude (small angle of swing) (1).The mass hanging on a spring is quadrupled. State the effect on the period of oscillation.
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The period doubles, because T ∝ √m (1).State two quantities that have no effect on the period of a simple pendulum.
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The mass of the bob (1); and the amplitude, provided the swings are small (1).A 0.50 kg mass on a spring of spring constant 200 N m−1 oscillates with SHM. Calculate the period.
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T = 2π√(m/k) = 2π√(0.50/200) (1)
T = 0.314 s (1)Calculate the length of a simple pendulum that has a period of 2.0 s (g = 9.81 m s−2).
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From T = 2π√(l/g): l = g(T/2π)2 (1)
= 9.81 × (2.0/2π)2 (1)
l = 0.994 m (1)A 0.20 kg mass on a spring oscillates with a period of 0.80 s. Calculate (a) the spring constant and (b) the frequency of oscillation.
A mass on a spring (k = 50 N m−1) oscillates with an amplitude of 0.10 m. Calculate the total energy of the oscillation.
On a mountain expedition, a student sets up a simple pendulum of length 0.800 m and times 20 complete oscillations at 35.9 s. Determine the value of g at the site.
A 0.30 kg mass hung from a spring stretches it by 0.045 m (g = 9.81 m s−2). Calculate the spring constant. Go on to calculate the period of small vertical oscillations of the mass on this spring.
A mass on a spring of spring constant 80 N m−1 oscillates with amplitude 0.060 m. Calculate the total energy of the oscillation and the kinetic energy of the mass when its displacement is 0.030 m.
A simple pendulum of length 1.0 m is taken to the Moon, where g = 1.62 m s−2. Calculate its period there and compare it with its period on Earth (2.0 s).
A 0.30 kg mass on a spring of spring constant 120 N m−1 oscillates with an amplitude of 0.050 m. Calculate its maximum speed.
Describe the effect of damping on an oscillation.
A grandfather clock keeps correct time using a simple pendulum of length 0.994 m where g = 9.81 m s−2; its period there is 2.000 s. The clock is moved to a city where g = 9.78 m s−2. Deduce whether the clock now runs fast or slow, determine the time it gains or loses per day, and suggest how the pendulum should be adjusted to correct it.
A student sets a mass-spring system oscillating vertically in air, then repeats the experiment with a large card attached to the mass to increase air resistance. Describe and explain how the displacement-time graph and the energy of the system differ between the two experiments.
Liquid in a vertical U-tube oscillates with a period T = 2π√(L/2g), where L is the total length of the liquid column. Calculate the period when L = 0.30 m (g = 9.81 m s−2), and state and explain what happens to the period if a denser liquid is used with the same column length.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
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