Period of a mass-spring system - Section 12C

**1. **The hummingbird
makes a humming sound with its wings, which beat with a frequency of 90.0 Hz. Suppose a mass is attached to a spring
with a spring constant of 2.50 x 10^{2} N/m. How large is the mass if its oscillation
frequency is 3.00 x 10^{-2} times that of a hummingbird’s
wings?

**2. **In 1986, a 35 x 10^{3} kg watch was demonstrated in Canada.
Suppose this watch is placed on a huge trailer that rests on a lightweight platform,
and that oscillations equal to 0.71 Hz are induced. Find the trailer’s mass
if the platform acts like a spring scale with a spring constant equal to 1.0
x 10^{6} N/m.

**3. **A double coconut can
grow for 10 years and have a mass of 20.0 kg. If a 20.0 kg double coconut oscillates on a spring 42.7 times each minute, what is the spring constant of the spring?

**4. **The monument
commemorating the Battle of San Jacinto in Texas stands almost 2.00 x 10^{2} m and is topped by a 2.00
x 10^{5} kg star. Imagine that a 2.00 x 10^{5} kg mass is placed on a spring
platform. The platform requires 0.80 s to oscillate from the top to the bottom positions. What
is the spring constant of the spring supporting the platform?

**5. **Suppose a 2662 kg
giant seal is placed on a scale and produces a 20.0 cm compression. If the seal and spring system are set into simple harmonic motion, what is the period of the oscillations?

**6. **On average, a
newborn human’s mass is just over 3.0 kg. However, in 1955, a 10.2 kg boy was born in Italy. Suppose this baby is placed in a
crib hanging from springs with a total spring constant of 2.60 x 10^{2} N/m. If the cradle is rocked with simple harmonic motion, what is its period?