I am confused on how to solve this question, please explain in detail

Question

1. In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression,

x = 5.00cos(4t+(pi/6))

where x is in centimeters and t is in seconds

At t = 0, find acceleration of the piston

2.A light, rigid rod of length ℓ = 1.00 m

 joins two particles, with masses m₁ = 4.00 kg

 and m₂ = 3.00 kg,

 at its ends. The combination rotates in the xy-plane about a pivot through the center of the rod (see figure below). the speed of each particle is 8.00 m/s. What would be the new angular momentum of the system (in kg · m²/s) if each of the masses were instead a solid sphere 13.5 cm in diameter? (Round your answer to at least two decimal places.)

Answer 1

1. In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression,

x = 5.00cos(4t+(pi/6))

where x is in centimeters and t is in seconds

At t = 0, find acceleration of the piston

2.A light, rigid rod of length ℓ = 1.00 m

 joins two particles, with masses m₁ = 4.00 kg

 and m₂ = 3.00 kg,

 at its ends. The combination rotates in the xy-plane about a pivot through the center of the rod (see figure below). the speed of each particle is 8.00 m/s. What would be t

he new angular momentum of the system (in kg · m²/s) if each of the masses were instead a solid sphere 13.5 cm in diameter? (Round your answer to at least two decimal places.)

As 1 has already been answered, here is answer to problem 2

Angular momentum= I *w where I is moment of inertia

and w= angular velocity

I in this case = m₁ r₁ 2 +m₂ r₂²

Plug in m₁ and m₂ and r₁ = 0.5 m =r₂

Now w = v/r =8/0.5, Get Angular momentum

For solid sphere use I = 2/5 (mr² ) for each sphere and then move axis to center using Parallel axis theorem

I_effective = I + md²

Answer 2

In problem 1 you are likely missing the appropriate equations.

For an object with the formula for position as

x = A*cos(n*t + Φ)

The velocity and acceleration are

v = -A*n*sin(n*t + Φ)

a = -A*n²cos(n*t + Φ)

There is another equation if you start with sin instead.

Substituting A = 5.00; n = 4; and Φ = pi/6 and t = 0; you can find acceleration.

Note the negative.

You should get a number between - 50 and -100

because this is acceleration the units will be cm/s²