1) After landing on an unfamiliar planet, a space explorer constructs a simple p
ID: 1509231 • Letter: 1
Question
1) After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 54.0 cm . The explorer finds that the pendulum completes 106 full swing cycles in a time of 143 s .What is the magnitude of the gravitational acceleration on this planet?
2) An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( m = 0.13 g ) driven back and forth in SHM at 1.0MHz by an electromagnetic coil.
The maximum restoring force that can be applied to the disk without breaking it is 3.7×104 N . What is the maximum oscillation amplitude that won't rupture the disk?
What is the disk's maximum speed at this amplitude?
3) The amplitude of an oscillator decreases to 36.7% of its initial value in 22.0 s .What is the value of the time constant?
Explanation / Answer
1) given
Lenth of peundulum, L = 54 cm = 0.54 m
Time period T = 143/106
= 1.349 s
now Apply, T = 2*pi*sqrt(L/g)
T^2 = 4*pi^2*(L/g)
g = 4*pi^2*L/T^2
= 4*pi^2*0.54/1.349^2
= 11.7 m/s^2
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