I had that thought as well, so I tried using numerical values for the initial conditions as well and found the same error. However, it only occurs for certain numerical values used. For example, the following IC's return the same error message.
In[1]:= eqn1[g_, R_, t_] =
D[\[Phi][t], {t, 2}] + g/R*Sin[\[Phi][t]] == 0;
In[2]:= ic = List[\[Phi][0] == 1, \[Phi]'[t] == 0 /. {t -> 0}];
In[3]:= sol1[g_, R_, \[Alpha]_, \[Gamma]_, t_] =
DSolve[{eqn1[g, R, t], ic}, \[Phi][t], t]
During evaluation of In[3]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.
During evaluation of In[3]:= DSolve::bvfail: For some branches of the general solution, unable to solve the conditions.
During evaluation of In[3]:= DSolve::bvfail: For some branches of the general solution, unable to solve the conditions.
Out[3]= {}
As do these IC's:
In[1]:= eqn1[g_, R_, t_] =
D[\[Phi][t], {t, 2}] + g/R*Sin[\[Phi][t]] == 0;
In[8]:= ic = List[\[Phi][0] == \[Pi]/16, \[Phi]'[t] == 0 /. {t -> 0}];
In[9]:= sol1[g_, R_, \[Alpha]_, \[Gamma]_, t_] =
DSolve[{eqn1[g, R, t], ic}, \[Phi][t], t]
During evaluation of In[9]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.
During evaluation of In[9]:= DSolve::bvfail: For some branches of the general solution, unable to solve the conditions.
During evaluation of In[9]:= DSolve::bvfail: For some branches of the general solution, unable to solve the conditions.
Out[9]= {}
However, some IC values do work:
In[1]:= eqn1[g_, R_, t_] =
D[\[Phi][t], {t, 2}] + g/R*Sin[\[Phi][t]] == 0;
In[14]:= ic = List[\[Phi][0] == \[Pi]/10, \[Phi]'[t] == 0 /. {t -> 0}];
In[15]:= sol1[g_, R_, \[Alpha]_, \[Gamma]_, t_] =
DSolve[{eqn1[g, R, t], ic}, \[Phi][t], t]
Out[15]= {{\[Phi][t] ->
2 JacobiAmplitude[
1/4 (-((Sqrt[2 (4 - Sqrt[2 (5 + Sqrt[5])])] Sqrt[g] t)/Sqrt[
R]) + 1/2 Sqrt[
4 - Sqrt[
2 (5 + Sqrt[5])]] (12 Sqrt[4 - Sqrt[2 (5 + Sqrt[5])]]
EllipticF[\[Pi]/20, 8/(4 - Sqrt[2 (5 + Sqrt[5])])] +
4 Sqrt[5 (4 - Sqrt[2 (5 + Sqrt[5])])]
EllipticF[\[Pi]/20, 8/(4 - Sqrt[2 (5 + Sqrt[5])])] +
3 Sqrt[2 (5 + Sqrt[5]) (4 - Sqrt[2 (5 + Sqrt[5])])]
EllipticF[\[Pi]/20, 8/(4 - Sqrt[2 (5 + Sqrt[5])])] +
Sqrt[10 (5 + Sqrt[5]) (4 - Sqrt[2 (5 + Sqrt[5])])]
EllipticF[\[Pi]/20, 8/(4 - Sqrt[2 (5 + Sqrt[5])])])), 8/(
4 - Sqrt[2 (5 + Sqrt[5])])]}}
As does pi/2:
In[1]:= eqn1[g_, R_, t_] =
D[\[Phi][t], {t, 2}] + g/R*Sin[\[Phi][t]] == 0;
In[25]:= ic = List[\[Phi][0] == \[Pi]/2, \[Phi]'[t] == 0 /. {t -> 0}];
In[26]:= sol1[g_, R_, \[Alpha]_, \[Gamma]_, t_] =
DSolve[{eqn1[g, R, t], ic}, \[Phi][t], t]
Out[26]= {{\[Phi][t] ->
2 JacobiAmplitude[
1/2 (-((Sqrt[2] Sqrt[g] t)/Sqrt[R]) + 2 EllipticF[\[Pi]/4, 2]),
2]}}
Having tried multiple IC values, more values seem to yield error messages than not. This does not surprise me for the derivative initial condition, as I don't think a full analytical solution exists for non-zero values of that, but the initial angle should be able to have any value of 0 to 2*pi and yield a solution, no?