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Which of the following is true of all systems displaying simple harmonic motion?

SELECT MULTIPLE OPTION

A
Movements is always up and down.

B
Movement is always side to side.

C
All SHM systems are man-made.

D
Simple harmonic motion is that the resistive force acting on the object is proportional to the object's displacement from equilibrium position.

E
For all SHM systems, the amount of force restoring an object to its equilibrium position is proportional to the amount of the object's displacement from equilibrium.

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Text SolutionText solutionverified iconVerified

The basic necessity for a motion to be called a simple harmonic motion is that the resistive force acting on the object is proportional to the object's displacement from equilibrium position. Hence
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Texts: 5. The Australia Telescope Compact Array in New South Wales consists of six radio telescopes that can be positioned along a 6 km long track. The intensity of an incoming signal is measured by combining waveforms from pairs of telescopes, known as baselines. If the telescopes are evenly spaced along the track (i.e. 5 baselines of length 1.2 km, 4 baselines of length 2.4 km, and so on), the total signal intensity is defined as: I = x6000 + 24800 + 3x - 3600 + 4b2400 + 5az1200 where I and a are the intensities measured by a single telescope pair for each of the five different length baselines.
  1. Derive a function F(k) for the observed image (in wavenumber space) by taking the Fourier transform of the signal intensities along the x-axis. What is the real-valued part of F(k)?
  2. What is the full-width at half-maximum (FWHM) of the approximately Gaussian telescope beam that detects astrophysical objects in the observed image F(k), given that the FWHM occurs when F(k)/F = 0.5? Assume the signal amplitude is the same for each baseline, i.e. a = s, and include a labeled sketch of FWHM. Use the approximation cos(θ) = 1 - (θ^2)/2 and remember the FWHM is the width between -k and +k.
  3. What is the angular size of this Gaussian beam if the telescope is observing at a frequency of 1.5 GHz? Give your answer in arcseconds. (1 degree = 3600 arcseconds). HINT: Use the relation θ = kλb/a, where k = 2π/c and λ is the FWHM of the telescope beam.
  4. The effective size of the telescope D is known to relate to the angular size of the beam as D ≈ 1.22λ/θ, for θ in radians. How does this effective telescope size compare to the 6 km longest baseline of the physical array?
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Question Text
Which of the following is true of all systems displaying simple harmonic motion?
TopicOscillations
SubjectPhysics
ClassClass 11
Answer TypeText solution:1
Upvotes128