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?

Answer 1

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